I was advised by one of the experts in this newsgroup that it needs a new motor (thank you, Todd).
After replacing the support roller wheels (all 4) - which was much needed, as each of the older ones was about 1-2 mm shorter (worn out) in diameter, the dryer's drum rotates much more smoothly and is certainly less noisy - but... the problem described above still exists.
So, I came to the conclusion that the expert is right and I am about to order a new motor for my dryer.
However, as someone who used to be familiar with the theory behind the operation of electric motors, I am curious what could make this motor behave so strangely. Isn't a motor either "dead" or "alive"? I could understand an unusual load (i.e. one that the motor was not designed for) overloading the motor and leading to its thermal protection to shut it off. But now, all is supposedly well - so why would it overheat?
Could this be indicating some additional *mechanical* problem, stemming from some wear in the motor assembly itself? (after all, it is 12 years old)
Just curious. I would appreciate any tip or hint in this regard.