I'm with lomapaseo. The problem is rate, not temp. Tightly packed granular microcrystalline water ICE will not conduct heat well. Just as a solid crystal of quartz is a nice heat sink, sand is not. Besides, the crystals only melt to form ICE, they have no exit. So the problem is to expel the 'pack', not prolong the obstruction by trying to 'melt' it? Heating the Stainless steel is a waste of energy.
Some way to expel the slug of compressed particles? compressed air, forward?
A snow cave is great insulation against a bitter exterior, as loma has said. Heat is slow to escape, why would it be quick to enter? Some new approach is needed, it is taking too long to fly without Pitot tubes?