My thermostat to heat pumps 7 wire cable would not support many amps. I think they mostly just convey "signals and information" (fan, heat, cool 'triggers') and the power to run the AC functions is wired at the AC.
So I don't think it is a good idea to use that cable for powering anything else.
If, however, that 12v continuous wire is a 14 gauge wire or better then it might be a good place for sourcing your 12 volts. First you'll have to determine what it is for and if the fusing of that circuit will support a fan. If it's a switched circuit you might need to find another source.