The reel motor that controls the RW and FF is not driven by a belt, and no the deck does not get hot. It's not a huge differerance between cold and warmed up.It rewinds and fast forwards very fast and smooth otherwise...
Could just be natural age in the drive circuitry then.
If it's smooth and only slight, I wouldn't worry about it.
I've seen decks do this before after sitting around for ions
and then it goes away. Some tapes ... especially some esoteric metals -
have really tight construction that can tax a mechanism. If you ever
stumble upon a used MA-XG Fermo, Sony Metal Master or Maxell Vertex,
those can be used to demonstrate a tired deck and/or one with wearable
coupling components that need attention.
What's your deck again ?