do you have the electrical schematics for the heater circuit ?
many of these blower motors are multiple windings
speed is selected by the switch chossing the correct winding sequence
if this replacement motor was mis-wired when installed
it could create this problem
power use will be higher with engine running and 14+ volts from alternator
FYI 'Society of Automotive Engineering' wire is smaller than the same gauge Commercial wire
the problem 'appears' to be reistance at the fuse holder creating heat
i saw a similar problem, where a fuse holder with 40 amp load and 60 amp fuse and 4 guage wiring
the fuse was melting, from the blades getting hot
'Chinese' fuses with poor medal bad electrical conductivity aka too much resistance,
in the fuse 'blades'