I'm using a PTC heat tape, [which needs no stat as it self regulates], to keep vegetable-oil fluid by tracing the oil lines. Similar problem, except that the oil forms crystals of fat rather than ice. These tapes don't get particularly hot & various grades are available. The main problems I encountered were that the stuff is not very flexible- it's difficult to manipulate to the route you want and has a minimum bending radius. The other problem was 'ending-off' and connecting to the power supply. My supplier provided a 'kit' [hahaha], comprising shrink-tube, self amalgamating tape and capping, which proved to be a nightmare demanding Astronauts skills, a hot air gun and 3 pairs of hands! End result looked clumsy and amateur despite my best efforts. The tube-runs also need an insulation tube over, as the power is just a few watts per foot. Add a necessary weatherproofing layer over that in your scenario and my crystal ball predicts a cornucopia of expletives issuing from the general vicinity of the electrician.
