That plug is done. Time to stop using it. It's getting hot and melting the plastic.

I'd also be concerned about the condition of the wall outlet where this was plugged in. The outlet may be due for replacement as well.

It is possible to replace the plug on the cord, do so at your own risk. Use a commerical/industrial grade polarized plug on it, Leviton MS2-P is my default choice for this application. (not available in the box stores.) Note which wire wire is attached to the wide blade. Be careful stripping the wires, not to cut strands of wire off. Make sure the termination screws are tight.