Reddit mentions of Honeywell 802360JA Motor

I'm a little late to the party but I'll offer my advice just in case you still need help.

From the other comments I understand you have a thermostat with a mercury bulb in it. This means you don't have electric baseboard but rather hot water heating baseboards. All the wiring is low voltage which means you don't need to worry about zapping yourself.

From the sounds of it your thermostat is working. I would assume then that your zone valve is stuck open now. A zone valve is a mechanical device that opens and closes the flow of hot water through the baseboard piping. 9 times out of 10 the zone valve motor gets seized open or closed, open in your case.

http://www.homedepot.ca/product/honeywell-motorized-zone-valve/903029

The above image is what the most common zone valves look like. Under the removable cover is the motor. On the side of the valve is a small lever. If the lever moves side to side with ease then the valve is stuck open. I would then try replacing the motor.

http://www.amazon.com/Honeywell-802360JA-Replacement-Motor-Valves/dp/B0006UPLQC

This is what the motor looks like. Any hardware store should carry a replacement. All you have to do is remove the two screws that hold the motor in place and you can pull the motor up. Sometimes the motor might need a few wiggles to get it loose, but don't worry about that. You just put the new motor in place, the two screws, then connect the two wires.

edit: put the same link in twice, fixed it to show the motor

One tip about the screws for the new motor is if it is hard to get the back screw in don't worry about it. I leave the back screw out all the time if I can't get to it easily. It only needs the one screw to hold it in.

I hope this helps. But in reality I hope you have already gotten the problem fixed. If so, no worries. Good luck.