For a heat source I have used wet/dry heating pads wrapped around the carboy and held in place with elastic bands for years. Like this
. My shop gets below freezing in winter and I find that set on low, the heating pads have no trouble keeping wort at ale temps in the cooler.
Also one thing it took me a while to figure out is that when you direct wire the compressor to be controlled by an external controller, you are disableing the internal thermostat. So there is no need to put it on any setting because it doesn't work anymore.
If you want the light to be functional, you can splice the power wire into the compressor power wire and the light circuit. Just be sure to cap the wire that is left that you cut to the compressor to make the splice because it will be hot when the internal thermostat calls for cooling. Of course the light will work only when the compressor is on. I have three different wine coolers and the wiring colors are different for all three, so you will have to look at the wiring diagram on the back of the cooler to decide where your wires need to be cut/spliced.