Is everything else in rig working? If so then it is probably not the converter.
First thing I would do is check the fuse by pulling it inspecting and replacing then check for 12 volt at the furnace. If you get 12 volt to furnace then bypass the thermostat with a jumper wire AT THE FURNACE. Check to be sure all connections are secure and clean.
If this does not work then get the model # of the furnace and someone here will have the troubleshooting guide or you may have one in the paperwork.
Traveling with my best friend my wife!