current is not measured by feeling wire temperature, even then we don't know what is the size of the wires.
do you have some current readings with and without load?
i am still firm believer that this motor is toast... why don't you open it and take a look at windings and brushes. they must be mess.
one of my colleagues decided to fix kids 'barbie car' and replaced the busted motor with one from power seat (we had lots of those).
it worked fine for little girl, it even worked for bigger girl who really took it for a spin (off road, up and down hill then through the bushes,).
well, it worked for good 20 maybe 30min and that is when the motor melted (most car motors like seat, mirrors, windows etc are not rated for continuous duty).
windshield wiper motor is rated for continuous duty but since already geared, speed is low.