The control board does control the furnace from the T'stat. Depending on the make of furnace you have, there are a couple ways the furnace can be controlled via a thermostat. Hopefully the control board has a bad compressor relay causing the unit to run when off and a new control board should resolve the problem. There are some pdf files iRV2 Forums - Files - Heating and Cooling
that may help. Let us know if you have a Suburban furnace and we can get a file put up or sent to you. Good luck and keep us posted.
Mike, RVIA & RVSA Certified Master RV Technician
Amy, Dr. Assistant - Roxie & Mei Ling, four legs each
2000 Gulf Stream Scenic Cruiser 450 hp & 1330# torque
06 Saturn Vue, 06 Chevy Z71 4x4 & 2014 Corvette Z51 M7