Jake's confidence is appreciated but misplaced in this instance... Problem is there's no "instrumentation" that can tell that the clouds... etc. Secondly, if we knew the weather conditions that are producing the clouds (type of fronts) we could then determine if we should climb or descend. Lacking any further information my best guess is the pilot should bend over and kiss his rear a solemn goodbye... because, in a short while he'll just be along for the ride...
JTP is on the right track about the adiabatic rate (it is 2.7 degrees C per 1,000 feet in dry air) but the problem is one would have to raise the temperature significantly above freezing to get any immediate relief.
High speed fighter aircraft could conceivably fly fast enough to compress the air sufficiently on the leading edges of the wings and tail to melt any ice accumulation... but that would be very fast indeed, although less than the speed of sound...