I've installed a dedicated 20 amp circuit for a heater/fan/night light/
light combo. Naturally, I used 12 gauge wire to deliver the power to
the unit. But I am faced with this problem. There are four sets of
wires that need to run from the switch box to the unit which means a
total of five sets of wires which the box just won't take.

Is it OK if the unit is connected to the switch with 14 gauge wire. Or
if I use 12 gauge for the heater part and 14 guage for the rest?

Simple answer? No... If you have a 20amp breaker you cannot use ANY 14
gauge wiring in that circuit.

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