If your heater is separate from your AC unit,meaning the heatewr blows through floor vents, you might look at this. Mine did the same thing and I had the fan position in high and/or low and not in the auto mode.With the AC on it kept running, it was here in Texas. When I went ot auto, the furnace worked without the fan on the AC working.Check to see if this will help.
2012 Super Crew 4WD 6.7 PSD
2015 Cardinal 3800 FL
2007 Road King Black Cherry-Hers
2007 Road King Blue-Mine
1979 FXS Hot Rod Shovelhead