You'll be OK, run the cable.
If the heater is off, there's no current flowing through the heating element. Even if it's on, most category specs (and transceiver specs) can easily overcome the common-mode noise.
Conventional wisdom applies: If you can avoid it, avoid it. If you can't, you can't. Near an active heater is not the preferred route, but if it's all you have, go with it, and do whatever you can to avoid the fire hazard (plenum cable might be a plus here).
Impulse noise (like flourescent light baluns, electric motors, etc) are more of a threat to your signals than a constant 60Hz hum.
FWIW
Scott