2000 S-Type 4.0 V8 running hot and overheating

I just picked up a 2000 S-Type with 70k miles. The last few days I noticed the radiator fans coming on more frequently after the car was shut off. I do not drive the car more than 10 miles a day at regular city speeds (35-45 mph). It will be running fine than quickly the engine temperature will move up to the red zone and the High Engine Temperature Warning comes up on the dash. Just as quick as it heats up the temperature will go back down. The radiator cooling fans seem to run at all times now. I have checked all the fluids and they are at normal levels. Am am thinking it is related to the thermostat but I am not sure. I live in a small town the nearest Jag dealership is 80-100 miles away. Any imput to help diagnose the problem would be appreciated.