97 Pontiac Grand Prix

I have a 97 pontiac grand prix. 158,000 miles, automatic, 3.1 liter. The problem is this. The temperature gauge keeps moving up and down as I drive the car. While the temperature gauge is going up, I have no heat, while the gauge is going down, I have heat. I does not go into the red zone, but comes close and then goes back down again. This happens at any speed. I have replaced the thermastat and flushed the radiator. Also the air conditioning is not working at all, this just happened after replacing the thermastat. Don't know if its related or not.