I rented an old farm house way back in the day and the insulation in that place was pretty much nonexistent. The insulation was newspaper. I had to deal with a frozen sink pipe all the time, on a north west facing wall. I would put a space heater near the opening and let it do its thing, which always cured it but what a pain. I would use some kind of pipe wrap when it's thawed, or go with something like this, if you have an outlet near?
