2002 Nissan Altima Tempature Gauge

Hi, my car has never given me mechanical problems until today. I was just driving my car normally, then all of a sudden when I was going slow and tried to accelarate, it stuttered like it was running out of gas or there was water in the spark plugs and it did this every time I would hit the gas pedal. It would cruise fine but not accelarate without stuttering. So I parked it and reved up the engine and still did the same thing. So I turned the car off and cranked it back up and it was perfectly fine. But then I looked at the tempature gauge and as it was idle it would go to H and as I would give it gas it would go back to the middle, but as I drive down the road it would just go back and forth. I made sure there was coolant in the tank and there was and there are no leaks. Someone said that it could be the thermostat stuck but I just need to know if need to take it to a mechanic. If you could help me please!