Not to hijack but we had a refrigerator in our garage that would freeze up. As it turns out, the service guy added a small heating element to the coils and it works fabulously now. I wonder if something like that could be added to yours?
You should be able to accomplish the same thing by adjusting the heater valve (or adding a small bypass) to never be all the way off, always leave a little hot water flowing through the coils.