I play a zither, not a guitar, but it goes out of tune with temperature changes so I'm very aware of this problem.

Not sure where you keep the guitar case, we try to put the zither directly on the back seat which cushions it from the road as well as heat from under the car. If it is riding in the [station] wagon area, I usually put blankets or foam under the case to protect it from heat transferred from the car's exhaust system.

I cover it with a loosly folded white "down" comforter, then with a reflecting cover (we use the kind that are made to put on a car windshield.) The comforter can insulate it from heat just as well as from cold. And of course it makes a heap that doesn't look at all as if the car contained an instument which is another plus.

Well this is all very low tech but it works well.