I used this stuff on F15 jet engines while in the Air Force.  It was used to add abrasion and heat resistance to wiring harnesses, etc.  It was black silicone and was called F4 tape, IIRC.
  I still keep some in my toolbox for various automotive uses.  You could use it to temp repair a coolant hose, I suppose.  But, even if you wrapped it around the pulleys a hundred times, I doubt that it would be strong enough to stand in as a fan belt.

Mike B.