I live in Assisi. I find that Air-conditioning is necessary for me during all of the summer and early fall months. This week it was over 95 degrees here. This summer the temps ran easily in the low 100's with high humidity.
BUT most Italians will tell you differently-but they will also have their entire house shut up during the day, opening the shutters and doors in the evening and closing again in the early morning. And, they don't go out as much if unnecessary.
I have not been to Torre di Conti, nor have I heard of anyone staying there. That does not mean it isn't good. The price is WAY CHEAP.
I rent out my apartment here in Assisi when I am away traveling but it is within the city walls. There is a place called Villamena that is about 10 min. outside the walls of Assisi in the country. It is vacation rental apartments with huge pool. The owners are lovely people-speak English pretty well.
I know that Anne Robichaud-the American who has lived here for 30 years-a guide...offers to find accomodation from her website. You might want to contact her. She may know of this place you're mentioning or give you some other ideas. www.annesitaly.com
Please feel free to email me directly if you'd like any help...