Chosen Solution

The cord heats up when it first starts washing

Most likely a short in the wiring. A cord heats up because of excessive current running through it. It means that you are drawing near maximum rated current. It is somewhat normal for a cord to get WARM for an appliance that uses significant power like a heater or a motor. If a cord gets hot, you are probably exceeding the rating for the cord.

The motor could have worn brushes. Try smaller load to see if if you get the same effect. Also check that inlet hoses are not blocked or kinked making the pump work harder. Clean dust/dirt from motor casing if needed. Plug into a different outlet via extention cord to see if you get the same effect.