1995 Oldsmobile Cutlass Cierra headlights go out

1995 Oldsmobile Cutlass Cierra 2.3 mileage: 86,000. I have replaced the dimmer switch which is also the headlight switch, and the turn signal twice now. It seems that when my heat is on for any extended period, my headlights go out; not the parking lights or interior lights, just the head lights. Please help! That includes the brights too. If I turn the car off for a while to cool, they work again.