Room above driveway is warmer

It is almost ALWAYS possible to insulate a carport ceiling, one way or another - and it WILL be more effective than insulating the ceiling (which could very well already have been done) The difference in temperature is due to the heat radiating from the driveway - so the only way to attack the problem is to reduce the amount of that heat getting into the room.

Boy, that construction is the EASIEST to insulate. Stuff the space between the joists with insulation, and tack on a layer of plywood or sheathing material of your choice. When you have a finished ceiling, or essentially a huge soffit, it is a little more involved - but still not anything close to impossible.