Turned the thermostat on to get some heat. After the room warmed, turned the thermostat off. Although the thermostat was turned to off, the temperature rose to be over 90 degrees. I decided to check the furnace and turned the gas cock off because I didn't want to produce any more heat. Could someone tell me what they think could be the problem?

Best guess, since I know nothing about your furnace from your post, is a bad gas valve.