Air conditioning in Rome in July

I assume it is common. And it may not turn on till late morning. We have encountered that before. Lots of places are very energy conscious. Many will have card key that fits in a slot by the front door. When you leave and pull the card from the slot all electric - lights, AC, etc. - turns off till you return and replace the key. And we have also found that the standards for AC is not the same as you would expect in the US. Don't expect 72 degrees - maybe 80.

I have the same information as Frank..
In hotels, instead of the apartments, you may have a little more control than in an apartment that is centrally air conditioned--but even in hotels, due to the high cost of electricity there, you're not going to get the kind of temps, or control, that you get in of a typical budget motel room here.

So know before you go: you're unlikely to be sleeping in air-conditioned comfort.
It will be muggy. Unless you go to the Ritz.

And the problem with many windows in Italian lodging is: they don't seem to come with window screens. So for night-time sleeping, after the AC is turned off by the building control system, if you open the windows you may just have unwelcome flying insects buzzing around.

I don't know your level of travel experience so forgive me if this is something you know already...

Nobody in the world uses air conditioning to completely chill a whole house to 65 degrees, the way that Americans do. Most european countries have a "climate control" that does little more than provide some circulation and dehumidifying effect.

There are hotels AND apartments that allow you to control the AC on your own. Do NOT stay in a place where the AC cuts off at night unless you want to be miserable.