It looks like theres a sheathed harness that runs up over the foam block under the blower to supply switched power and a ground, see if you can get it unplugged and probe it with the switch on for a 12vdc reading. Low voltage on the incoming side of that circuit would heat things up in that fan winding and so would a bad ground that's pinched or has some point of resistance in the circuit. You could just need to clean the plug up and use a little dielectric grease to restore the connection.
If your getting a voltage reading much lower than what the battery is providing in it's static condition follow that circuit back to the control switch and test on both sides of it, your switch may be bad and the ground lead should be checked for a pinched wire or loose connection.
If all else fails you can power the blower separately using your own fused pigtail and battery to see how it's working isolated from the circuit in the boat.
CAREFUL doing electrical work in your boat, that circuit all runs off the front fuse panel but you sure don't want to do anything to mess with the MPEM in the back of the boat, $$$$$$ for a used one if you could ever find it.
