Can't think of any direct connection between the two, but grounding problems usually cause weird symptoms. Unfortunately there are several grounding points, but if I were looking for one that might be effected by the heater being on, I'd pick the ones under the dash. The easiest way to get at them is to remove the dash cap and look for black wires connected to the fire wall, clean and reattach them. Also the ground lead v\from the rear of the intake manifold to the fire wall could be corroded. Some of the major grounds are; battery to engine block, engine block to frame, intake manifold to fire wall, under dash connections to the fire wall, lights to fender (near the front of the fender - both sides), fire wall to hood (passenger side).
Good luck,
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