Radiator fan won't shut off. 1988 Camaro

1988 Chevy Camaro, auto trans, 90,000 miles, 350 fuel injected. Question: What is causing my radiator fan to continue to run even after car is turned off. I parked car and heard the fan on after I turned my car off and thought it would shut off in a few minutes. I had to run in the house and came out 2 hours later and fan was still going. It drained my battery down and I couldn't turn on my car. Had to disconnect my battery in order for the fan to turn off. My neighbor was kind enough to help me but we are not sure what is causing the fan to continue to run. Jumped the battery and fan keeps running. Only way to stop it is to disconnect the battey or it drains current from my car. Does it need a new thermostat switch? Or what? I don't have a manual. Purchased the car used in 1996. Your help is very much appreciated. I can't donate at the moment, I only live on $200 a month before expenses. I was attacked by a large dog and am not working at the moment. When I can, I will send donation for your help.