I had the same problem after we first installed central heat. Heat tape wrapped around the PVC drain line DID solve the problem! I did have to thaw the pipe the first time with a heat gun but over several years have never had a problem since putting on the heat tape.
I don’t think heat tape would get hot enough to melt PVC, and some heat tapes have a thermostat that turns the tape on only when the temperature goes below 32. The packaging should have good info.
Scott