Engine Cooling problem
2002 Hyundai Sonata 4 cyl Front Wheel Drive Automatic 124300 miles

I have a 2002 hyundai sonata my temperature hand kept going up but never ran hot. Also if I turned the air conditioner on the hand would go back to the middle. I got a new thermostat because that is what the dealership said was wrong but the temperature hand continues to go up but not to the red area like it was previously and then eventually go back down. I just want to know what could be the problem now or is the thermostat bad?