Yeah warmth in the way you describe may indicate a problem. Do you mean the shore power wire, or the wire on the inside of the boat?
Warm is a relative term... the question is "how warm is warm"? My home vacuum cleaner gets a warm cord...
A few thoughts... I'm assuming this plugs into the AC line...
Did you put in new wire inside? What is the rating for the appliance? You may consider rewiring the panel, since a thicker wire will take more amperage. This would reduce fire hazards. The panel circuit breaker or fuse would still kick off at the published threshold no matter how thick the wire.
This is just a thought. The 30-year-old AC wire in my E27 is brittle and every exposed end has corrosion several inches into the (cracked) insulation. I am going to rewire this "before" I need to install the dehumidifier for the winter.
You didn't mention if this is a plugged appliance - also consider installing a GFCI plug on the AC line. That's cheap insurance right there... and also an early-warning device, because if the appliance continually trips it, then there is something that needs attention on the circuit.
Final thought - you said it was installed last Winter. If the appliance itself has a defective component, it could be drawing additional power. Maybe, maybe not, but it could be bad.
HTH,
- Jerry