You imply that you would have no heat from the furnace if the A/C blower
is running. That's not true. As Bluepill
suggests, the heater/furnace would still work even if the A/C blower is running. The A/C compressor is NOT running.
To all: as surprising as this condition appears to some, it is reported and solved 10-12 times per month here. One can search for furnace
and find many threads on same.