Just a clarification on 'conventional' airframe icing.
The risk is due to what is commonly called "supercooled droplets" - basically liquid water that is below freezing. When it hits a cold surface, it instantly freezes. At least according to the FAA regulations, 'conventional' airframe icing is a threat between +10 and -40 deg C, and below 23k (although it's been reported as high as 30k).
Ice Crystal Icing (ICI) is different - it's basically very small crystals of ice - typically at very high altitude (above 30k). ICI will simply bounce off cold surfaces, but can accumulate ice on warm (above freezing) surfaces because the crystals hit the warm surface, melt, then additional crystals cool the liquid water enough that it re-freezes and accumulates ice. Accumulations of ICI icing typically occur on surfaces between 0 and 20 deg. C. This is the issue that many engines have been having - ICI accumulates ice internal to the engine in areas where is normally too warm for ice to accumulate - when the ice sheds it can quench the flame (flameout) and sometimes damage compressor blades.