What temps are we talking about? There's a lot to consider here. AC 78 is different from Heat 78 as well as varying too much from day to night. As well as humidity can play a huge role. Cool temps with humidity will seem cooler and make the ambient air feel colder when warm temps and humidity makes its hotter because the moisture in the air is warm. If you can't let him outside and keep your house or apartment cool. I would suggest leaving a lower wattage basking bulb and heat pad to keep desired temperatures needed for your tortoise. So what temp would the AC be set at is the ultimate question?
I would do what Tom always suggest, which is a great idea. Use a thermostat or restate. Put a che on the reostat/thermostat for temps and use a regular house bulb for a basking spot.That will keep the temp in your torts enclosure at your set temp. The che will come on when needed. If your tort gets outside at least 3 days a week for some sun, you don't need to have a UVB bulb. If you need a UVB, get the long tube fluorescent kind that does not give off much heat, if any.