[dhoolwerf]

Try removing the blower motor (it's behind the glove box...not too difficult to extract), place it on the ground at the end of your driveway and blast it from all angles with your leaf blower. Clouds of carbon dust will blow out of it from the worn brushes. Then reinstall and see if it doesn't resume normal function. I have done this successfully on three different cars and it has worked each time. It's been a year since the blower motor quit on my 300C and I blew it out as described above. It's been working fine ever since.
The panel does get warm from the lights...that's normal and not anything to be concerned about.

 

[dhoolwerf]

Windings don't wear out; brushes do.

 

[dhoolwerf]

I assume the cage is not missing any vanes, and the air filter is not clogged? Is the replacement motor brand new, rebuilt or used from a junkyard? Not likely, but possibly the new motor is bad out of the box? Have you tried blowing out the old motor with a leaf blower and reinstalling it? That's worked for me on three different cars.