How do I reduce kitchen temperature during cooking?

Sucking hot air out of the kitchen using the hood ("chimney") will cool the room, though possibly not by much on a hot day. A nice big open window to allow fresh air in will maximise this effect. Even on a hot day, the hood will cause a through draught, and the lower humidity, slightly cooler air blowing over you as you cook will be much more comfortable.

In very rare cases where the outside temperature is above the inside temperature (traditional buildings that are designed to cool at night and heat as slowly as possible during the day) there's little you can do. Such buildings aren't really designed for use with air conditioning (and they often come from a tradition involving outdoor cooking)

Some other things you can do that make at least as much difference:

• Cover dishes when cooking and turn the heat down (yes, even if it's not traditional). This is especially useful when boiling/simmering as the steam contributes to the discomfort.
• Some dishes can be brought up to boiling point then insulated to continue cooking.
• In a heatwave I've been known to get a long extension lead and an electric hotplate and cook outside (probably not an option in an apartment unles you have a balcony).

Thanks for your clarification of 'kitchen chimney'. A lot of the readers of this SE come from places where it would be called an 'extractor hood'.

In my experience, an domestic extractor hood which draws air to the exterior of the building can really help remove steam, and oily vapours / occasional smoke from searing, grilling and frying. Their effect can be quite local to the hob; depending on how your kitchen is arranged, they can have surprisingly little effect on say. a separate oven. They can really help to keep a kitchen clean, reducing oily deposits around the room.

But I think they would have to move very large amounts of air (more like an industrial extractor) to have a significant impact on temperature in the room. Also, before choosing one, carefully imagine the steps involved in cleaning and maintenance, so you can be sure they suit what's available to you.

The best way to cool your kitchen would be to create a through draught, moving large amounts of air from a cooler place, through the kitchen, and out again. You will have noticed that sometimes, to cool a room, it's not enough to open one window in it - you must also open another window on the other side of the building. You have exhaust fans fitted, you say there is only one window - make sure there is somewhere to draw the air from without resistance, maybe by opening/venting doors or windows elsewhere.

In the days before air conditioning, traditional buildings in hot places took advantage of these natural phenomena much better than they do now, making use of light and shade, water-cooled central spaces, and chimneys, to create flows of cool air. If there's any way you can emulate that, I would try it before resorting to A/C.

Cooking sous vide and using induction burners both reduce kitchen heat.

The term I am more familiar with is exhaust hood (there are also recirculating hoods). Sometimes they use the terms ducted and ductless.

A powerful exhaust hood is about 1000 CFM. A small kitchen 10x8x8 = 640. So it would turn over the air in less than 1 minute. That is enough to pull off some heat. Is it more than a couple degrees would be hard to say.

Humidity controller should drop the humidity but it produces heat.

Your refrigerator produces heat. Be organized and pull all you need in one sweep.

Let dishes cool outdoors (if you need them to cool).

An outdoor BBQ keeps the heat out of the kitchen.

Cook with lids when possible. Turn off the heat and let it continue cooking as it cools.

High end highly conductive cookware will have less lost heat.

A crock pot probably uses about the same amount of heat but if it is spread over 4+ hours it should have less effect on temperature.

The only way you are going to reduce the ambient temperature in your kitchen during the summer is with air conditioning. Yes, I know it is not the answer you wanted to read, but it is the reality.

I've no idea what you are talking about with a 'kitchen chimneny', but if it is some sort of exhaust, you have got to makeup the air it sucks out of the kitchen from someplace. Is that air in that 'someplace' hot to or even hotter?

Any appliance you think up other than an air conditioner is going to consume energy that euauals more heat.

A more long-term solution could be to invest in an induction range/cooktop. The lack of excess heat is one of induction cooking's lesser-known eco-friendly attributes. Traditional gas and electric ranges heat up the air around the pan, losing up to half their heat to the surrounding environment. Not a good thing for large kitchen spaces like restaurants and warm climates - which are often made hotter with cooking.

This means having to crank up the air conditioning (if you're lucky to have it) when you're cooking - but not so with induction, where all the heat is transferred to the pot and very little ambient heat is generated. So induction cooking essentially reduces the heat in the kitchen.