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OK if only blows fuse in heat mode lets start by doing this. (Get a few fuses to troubleshoot). Then disconnect thermostat wires at furnace board and jump R to W on board to see if fuse blows.That will let us know if issue is in furnace or external circumstance such as wiring or thermostat.
WE can go from here anytime.Just come back when ready
Did you try the jumper between R and W to see if heat worked?
OK sounds like short is either in thermostat, or wiring between units . Go to thermostat remove all wires. Then touch R t Y and ac should come on.Touch R to G and indoor fan should come on.Touch R to W and heat shoud come on.Let me know if fuse blows any time.