If plastic on the outside of your power head is melting, then you probably have any issue with cooling. I would check to make sure the impeller is in good shape and probably replace it while you’re at it. Other sources of issue could be obstructions in the cooling jacket and obstructions to the water intake and the tube/line between the impeller and cooling jackets. I would clear these all out and replace the impeller, and you should not have cooling issues for a while.
"Outboards seem to multiply exponentially..........I find that for every finished project, there are two more waiting to be completed."