Flour and water... at which temperature?

Pizza Dough is usually a yeast bread so you want your water to be warm (100-110F) to activate the yeast without killing it.

Quiche crust, like pie crust, develops the best texture when the flour is mixed with the butter (or shortening) in a solid state, so you want to add other liquids at a cool temperature to prevent melting the butter to a liquid and creating a less flaky crust.

I am not really sure about tortillas, but with the first two examples you can see that temperature is important and differs from application to application.

I will answer for pizza and quiche, but I have never made tortillas, and have never researched what is important for them. And maybe we should split the whole thing into three separate questions, because the optimal temperature for each depends on different things.

pizza

Here, it is important to know what crust you are making. The two variables which will influence your choice of water temperature are how long you want to ferment the dough and how wet your dough is (with the gluten content of your flour modifying the results of wetness, so probably should count as a third variable).

Wetness is important because you want to be able to knead your dough. If you are working at normal hydrations (60 to 75%), any water temperature will produce a kneadable dough. If you are using very high or very low hydrations, you are concerned about your proteins not being able to form a good matrix, due to either not having enough water to absorb (low hydrations) or being mixed in a batter so wet that they can't hook into each other properly. Here, you can use the fact that gluten absorbs cold water much better than warm water. If you are working a hard dough, use warmer water, so the dough stays soft enough during the kneading. If you are working a very wet dough, use cold water. Shirley Corriher recommends throwing crushed ice into the food processor. This will give you stronger, better gluten.

Of course, it is not only the water temperature which determines whether a challenging dough will work well, it is also the protein content of the flour. The higher the protein content of your flour, the more water absorption you can expect. So, if you combine high-protein flour with cold water, you are likely to end up with a dough on the firmer side. If you are already making a low-hydration bread, it could be too firm for good gluten development. So, you may consider warmer water in this case. On the other hand, when you have a high-hydration bread, you are worried about the dough being too wet. You should use cold water then.

Beside consistency problems, water temperature will help you regulate fermentation. Yeast thrives at around 33-35°C (somewhere around 90-95°F I think). If you give it this temperature, you will have a very quick rise. Your bread will be ready in no time, but you will have a weak gluten and lots of quick-fermentation byproducts including thioles and ammonia. If you plan on a long rise, as usual for better breads, it is better to not induce quick fermentation through warm water. Use cold water or even try Corriher's ice advice if you are kneading in a mixer or food processor (I knead per hand, so I wouldn't use ice directly). Only warm the dough to room temperature for the final proofing. You can also use water anywhere on the continuum between these two extremes, or use a cold sponge combined with warm water. The temperature Cos Callis suggests is the lowest one if you want the leavening process to start right away, below about 20°C the yeast will work rather slow.

This advice is valid for any lean bread dough, including pizza crusts.

quiche

I assume that you are using pastry crust (as @Mien notes, some people pour the egg mixture over a yeast base). There are three basic types of pastry crusts: shortbread pastry, flaky pastry and raised pastry. For shortbread pastry, you are not mixing flour with water, you are mixing water with a smooth flour-fat paste. The temperature of the water makes no difference when mixing. You still want to have the pastry ice-cold when you put it into the oven, to prevent deformation, so it makes sense to use cold water. But if you make it with butter, it will be hard to shape when cold. If you prefer, you can use butter and water at room temperature, shape, then hold it in the fridge or freezer until it has hardened, then bake. Shortening is said to be more forgiving, I don't use it personally.

For flaky pastry, you are trying to create little pieces of butter or butter-flour paste encased in tender (but not gluten-toughened) flour-water sheets. If you make the flour-butter paste first and then add the rest of the flour and the water, you have more leeway with water temperature, because the well-buttered flour in the paste won't absorb the water even after the butter melts. The butter blobs won't fail to fatten its part of the flour , because they don't exist, you already have the paste. Also, you have enough of free flour in contact with the water to form the sheets before the butter has softened. Still, don't push it too far, up to room temperature is OK. If you use the traditional method of cutting coarse butter pieces into flour and almost mixing them, you should use ice cold water, and work quickly, preferably with cooled tools. This method involves pieces of pure butter which can melt and oil all of your flour before it has formed the sheets. Keep such dough cold at all times.

The third type is raised pastry. For this, you cook your water, throw the butter into the boiling water, and put the flour into the hot mixture. You get the separate buttery paste blobs and flour sheets because butter and water don't mix in the pot and some flour comes into contact with both. It also undergoes a starch gelatinization which doesn't happen with the cold methods. You should, of course, use boiling hot water for this type.