To be fair on both your point and the parent comment, it is both a difficult problem, and one that engineers at Boeing are capable of solving (and likely already solved). The issue here isn't an engineering one, it's a management one.
Looking it up the heating system uses bleed air from the engine so probably isn't as easy to control. On the other hand it just has to stop the thing getting hot enough to damage carbon composite which probably isn't anything extreme temperature wise. If you limited it to say 80C it would probably be ok to stop ice and also not fry the composite.