One of the characteristics of Ice Crystal Icing (ICI) is that TAT will read right at 0C (give or take depending on the sensor accuracy). The ice crystals will hit the heated probe, melt, then freeze again forming an ice cover over the probe with liquid water inside due to the probe heat. It's also unpredictable - it may not affect the aircraft probe, but affect dedicated engine probes, or any combination there of.
Ice crystals are also have low radar reflectivity, and don't generally show up on weather radar.