I have a forced hot air, oil furnace. When I bought the house, the furnace was shut off. It runs fine when I turn it on, but won't shut off. I think it's the thermostat - a round Honeywell, but I'm not sure how to test or replace it. Any help would be appreciated. Thanks, Pete.

Its either your thermostat or depending on its age a sticking relay on your furnace's control board.

To test the thermostat check for 24VAC voltage across your W and C once there is no call for heat.