How warm must dough be in order to rise?

Optimal yeast growth happens at around 37 degrees Celsius (98.6 degrees Fahrenheit), but dough will rise at any room temperature. As the temp rises, the yeast becomes more active, which is why you'll sometimes see recipes call over overnight rests in the fridge, where activity slows or stops. Yeast dies at anything above 50 C (122 F).

The important thing is knowing the temperature and, if you're really particular, the humidity in the air around your proof. This information is used for the sake of timing consistency, more than anything else.

As other answers have pointed out, most recipes tend to be calibrated to rise times which assume a temperature of 75-80 degrees Fahrenheit. (Professional baking recipes will actually specify a dough temperature after mixing and a temperature for proofing.)

However, the question also asks "how warm does dough need to be to rise properly"? If, by "properly," you mean "according to a recipe," then 75-80 F is a reasonable guess if temperature is unspecified. If the recipe mentions something vague, like "put in a warm place," that probably implies something somewhat warmer than 80 F, but it's always hard to know.

All of that said, bread dough can "rise properly" -- in the sense that it will eventually be ready to bake -- at a wide variety of temperatures. Both natural (sourdough) yeast and baker's yeast become mildly active when you get significantly above freezing, and they don't stop growing significantly until you get over 100 F. (For example, a growth curve for sourdough yeast can be found here.) From a practical standpoint, there's no good reason to go over 95 F or so, because both sourdough and baker's yeast hit their peak growth somewhere around 90-95F. Going hotter will simply slow things down and generally produce less desirable flavors.

Slower rises at lower temperatures can produce various useful characteristics, including increased flavor and better developed structure. Many recipes contain a required or optional "retarding" stage where the dough is placed in the refrigerator from a few hours to a few days for this reason. Yeast growth often doesn't completely stop even then, and some rise will be noticed over a long period.

The question brings up one final concern, since it mentions the timing of the recipe.

If you wish to prepare dough in the allotted recipe time, but your home is way too cool or too hot, what can you do?

There are three general approaches to this problem. Today, professional bakers generally use the first method, because climate-controlled equipment is easy to come by. But the other methods are still useful for the home baker without fancy equipment.

(1) Make use of a space at a more desirable temperature (as discussed in the question and some other answers). There are proofing boxes for home use with fairly precise temperature control, but most people make do with an oven that was slightly warmed and turned off, a microwave closed with a cup of boiling water placed in it along with the dough, simply putting the dough near a radiator or a warm stove, or some other makeshift device. (I sometimes used to cut off the top flaps of a wide but somewhat shallow cardboard box, tape up the bottom to "seal" it loosely, and invert it over the dough along with a cup of hot water, which I'd replenish periodically for long rises. This allows a lot of flexibility for different size boxes to handle everything from small to large batches of dough. Note that humidity as well as temperature can help rising.)

(2) Vary dough temperature. Particularly for a large batch of bread, it will take quite some time for the dough to cool down. Professional bakers have detailed calculations they use to vary the water temperature in order to arrive at an accurate final dough temperature. If you know your kitchen is 66, you might aim for an initial dough temperature in the 90-95 degree range, for example. The dough will gradually cool down as it rises, but on average it might end up with the timing of dough that was kept constant at 75-80. (This is obviously an approximation for ideal temperature, but so is putting a cup of hot water in a microwave or putting your dough near a radiator.) Rising rate can be somewhat regulated by varying the number of folds during proofing: more folding will redistribute temperature more quickly and lead to faster cooling.

(3) Vary the amount of yeast in the recipe. This one is particularly useful if you make a specific recipe again and again, but your kitchen is always too cold or too hot to get things done in the desired timeframe. Bakers often find the idea of varying a recipe to be distressing, since there is a common belief that baking relies on very precise measurements of ingredients. Making yeasted bread, however, is not a precise process unless you're doing it with professional temperature-controlled and humidity-controlled equipment. There's absolutely no reason to consider recipe quantities to be fixed in stone. For home bakers, it's often much easier to diverge a bit from the recipe than to recreate some "ideal" proofing conditions artificially.

Many people have attempted to create a dough model that would predict the amount of yeast needed for given temperatures. Considering the question deals with focaccia dough, this thread shows one person's detailed attempt to create a predictive model for pizza, which is often similar to focaccia dough in terms of hydration and other characteristics. (Here's the graph used to model activity of yeast at various temperatures.) Here's a similar model using sourdough instead of baker's yeast.

However, in the real world, dough rises at different rates depending on a number of other recipe details, from the type of flour to how much salt, fat, and sugar are present (if any). Studies often discuss how long it takes for yeast to double in number during a dough rise. I've seen various estimates that that time doubles for normal dough temperatures (say from 55 to 85 or so) every time you decrease the temperature by 7 to 15 degrees. That's a big range.

In any case, if you plan to repeat a particular recipe, but know your kitchen will usually be at 66 instead of 75-80, I'd try doubling the yeast for the recipe as a first guess. See how long it takes to rise, and modify as necessary. I've made these sorts of seasonal adjustments to recipes all the time -- I basically tend to use about double the amount of yeast on a cold day in the winter as I would on a hot day in the summer. If your goal is to have a predictable dough that can be baked on a specific schedule, this sort of modification may require the least fuss in the long run (unless you have an actual proofing box with precise temperature control).

I believe that the usual quote for rising temperature is between 24-29C (75-85F), though a little warmer than that I tend to use.

It's important that there are no draughts on the area, or you can have problems. My personal preference is to leave it in an airing cupboard, providing it is not too warm.

When making dough, The Bread Baker's Apprentice says to knead it until the dough's temperature (which those of us who are obsessive will actually take) reaches 77-80 degrees F. What you do from there may depend on what you are trying to accomplish.

For a consistent, speedy rise, your warm oven trick is perfect. This works well with sandwich breads and loaves which aren't intended to have big, crusty holes.

For hole-y crumb breads such as Italian bread, you want a cooler rise than a warm oven. This is because those big holes are encouraged by a long, slow rise, a light tough, and another long slow proof. In this case perhaps sticking it on top of your warm oven where it will get some heat or in a corner of the house near a vent where it is in the low 70s is ideal.

Typically, the rate of metabolism, in this case CO2 production, doubles for every 10°C rise (18°F) in temperature.

The Q10 temperature coefficient is a measure of the rate of change of a biological or chemical system as a consequence of increasing the temperature by 10 °C. ... For most biological systems, the Q10 value is ~ 2 to 3.

So dough at 30°C will rise about 4 times as fast as dough at 10°C, and dough at 70°F will rise about twice as fast as dough at 50°F.

Traditionally, doughs 'rose' (or proofed as is the professional term), in proof-boxes, which were nothing more than a set of big wooden drawers just like the ones you keep your underwear in. They are at room (shop) temperature, and have no special temperature or humidity controls. So if you can replicate that, you're on your way.

I grew up on a farm, and when it was sunny, my grandma always placed the bowl containing the dough, covered with a damp towel, into a sunny window. That's the method I've been using for a long time, works without problems for me. Putting it in a warm oven may be your best bet if the sun's not shining or you're in a hurry.

I proof my dough at 75 to 80 degrees Fahrenheit (24 to 26 Celsius).

To keep the temperature constant, I place my dough in a large cooler with a 10 to 15 watt light bulb and a thermometer. I can then prop the lid open to various degrees to get the right temp.

27 degrees C is optimum temperature

I am baking Christmas Stollen for 64 years and the rising changed every year. I found, that a heavy dough like Stollen needs a bit more than 100 Celsius. I also discovered that if I put my Stollen into a cold oven, not preheated it will rise quite a bit more. I just have one in the oven and it is rising beautifully. I used to try water at the bottom, but the Stollen gets pale at the bottom. Now I use Saran Wrap