I propose a tripartite model of empathy, roughly corresponding to Freud’s postulated id, ego, and superego. In this model, normal empathy is comprised of three components: instinctual, emotional, and cognitive. Children develop empathy in three phases which correspond to these three components, constructing the emotional and cognitive tiers upon an instinctual firmament. In adults, cognitive empathy always goes hand in hand with the instinctual element and the emotional correlate/component.
Cold empathy is not the same as merely cognitive empathy, though. It is intuitive: it is the residual instinctual component coupled with cognitive empathy, but divorced from and leapfrogging the emotional constituent. Cold empathy is the ossified consequence of “arrested empathy”. It is a predator's "empathy". It is all about resonance, not about "putting yourself in other people's shoes".