I have a 2004 Nissan Sentra and am having a problem with the car "jolting" or "pulsing" as it is accelerated either uphill

I have a 2004 Nissan Sentra and I am having a problem with the car "jolting" or "pulsing" as it is accelerated either uphill or between 2500 and 3000 RPMs on the highway. It seems to lose power and fills like there are only spurts of gas getting to the engine. As I drove the car and it was jolting, I noticed that the temperature gauge was on “C” even after I had been driving on the highway for 10 minutes. I stopped and turned off the car and restarted it. The temperature gauge crept slowly up. I began driving and when it began jolting again, the temperature gauge went crazy. It would rise to half-way then to “C” then to ¼ of the way. It would move frequently in an odd pattern.
I have had the check engine light on for the past couple of weeks. I had it read and the code given was for a bad thermostat or thermostat sensor. I changed the sensor but the light did not go away.  Could the jolting be caused by the thermostat sticking and not allowing the circulation of coolant?
I read something earlier about the Mass Air Flow sensor not being properly grounded and therefore not sending proper signals to the ECU. Could this alter the thermostat sensor?