Sounds like a thermostat problem, that is the only common point in the wiring of the two systems as far as I know. Can you just pull the circuit breaker for the AC for now?
If that doesn't do it, take the 'stat off the wall and disconnect the low voltage wires for the heat strip. Tape them so they can't short out. Refer to your manual for the diagram. I don't have this setup.... "Mouse" has a 1950s style mercury thermostat for the furnace and no heat strip. Crude, but 100% reliable.
Good luck.
John Davies
Spokane WA