You need to cut one of the red or black wires, probably the thin ones. I would guess that the thick ones are the incoming power and the thinner ones go to the door heater. Even with the light disconnected, the heater is still active as they're connected in parallel.
If you want to be extra clever, you can get a small toggle or other switch and install it in the sloped bit of plastic under the door switch and wire it to switch the heater on and off. It would presumably get inserted in the thin red wire. (If doing that makes the new switch also switch the light on and off, it should instead go in the thick red wire.)
