Very cold weather, toilet overflow, sink too

We use heat tape ( not wrapped - per instructions installed straight down the hose) with foam pipe insulation over. We have also been below freezing too many night to count with some days not much above freezing. We have used this method 3 winters now (Alabama & Mississippi) with no problems. We had frost free connection in Alabama, but not here. We had enough heat tape that we also went up the pipe to the faucet to keep that warm. The very first year we did have something freeze and the toilet almost overflowed. Stuff didn't want to go down -- turned our furnace on - let it heat up good and a couple hours later it worked fine. Don't know what froze, but we now leave our furnace set on 50 at night so it will run some during the night and keep everything warmed up.