1997 Other Honda Models Fan stays on

While visiting some friends for over three hours this evening on a cool night we returned to the car to drive home and noticed that the cooling fan was still on. We drove home 2.5 miles without incident and I had to disconnect the battery to stop the fan from running continuously. I opened the radiator cap and found the coolant to be full and cool. It was not heated up. The heater in the car worked well all the way home driving for no more than say 12 minutes. Should I replace the thermostadt or can you think of anything else that I should attend to. I am grateful for your response. Jim Cassidy