Welcome to the forum Barf.
Spaceballs Fan?
300.3(C), FPN does not allow the thermostat wire in the supply.
FPNs do not allow or prohibit anything.
FPNs are not code.
We could say 725.55(A) prohibits it but that is not entirely correct either.
There are ways to code compliantly run the the control circuit in the supply raceway.
But in general it is easer to keep them separate than to jump through the hoops needed to combine them.
