Dingo's response gets at some of the questions I'd ask. If you actually plan to make this device and use it then it would seem that much more needs to be done. If it's a class project that is supposed to be simple then some simplifying assumptions can be made.
If the fan simply stirs up the air in the room and you want more movement as it warms then the task seems simple enough. The people density might be a challenge - sensing someone passing an opening isn't tough but knowing whether they entered or left isn't as easy.
If you are bringing in air that is cooler, in order to cool the room when people warm it up then that's one problem. If air that you might bring in isn't cool, or is actually warmer, you might need to account for that.
Some building codes allow carbon dioxide sensors to control the fresh air that must be brought in - some codes do not allow it - if the room is occupied it must be ventilated regardless of activity level. Some municipalities look closely at this - others do not.
Don't forget that along with people, lights, computers, etc all produce some heat that can warm a room.