Is there a word for "cold" empathy?

Solution 1:

In your example, the closest idea of someone who may feel empathy, but may behave in an emotionally detached manner is a medical doctor or an emergency worker or another who must manage feelings and keep their focus on making good decisions. Some people call this detached concern. I would have said this isn't empathy and that cold empathy is an oxymoron. I just wrote an answer to that effect, but then looked a bit further.

More relevant to your question, however, is psychologist Daniel Goleman's article on social intelligence. What you call "cold empathy" Goleman calls cognitive empathy. He contrasts this term with compassionate empathy that involves understanding another in a more positive, engaged way. He also mentions emotional empathy in which feelings dominate and may cause overload and burnout.

The first [type of empathy] is “cognitive empathy,” simply knowing how the other person feels and what they might be thinking. Sometimes called perspective-taking, this kind of empathy can help in, say, a negotiation or in motivating people. A study at the University of Birmingham found, for example, that managers who are good at perspective-taking were able to move workers to give their best efforts.

But there can be a dark side to this sort of empathy – in fact, those who fall within the “Dark Triad” – narcissists, Machiavellians, and sociopaths (see Chapter 8 in Social Intelligence) – can be talented in this regard, while having no sympathy whatever for their victims. As Paul told me, a torturer needs this ability, if only to better calibrate his cruelty – and talented political operatives no doubt have this ability in abundance.

Solution 2:

Here's my first answer that said cold empathy is not possible.

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No, there is no such thing as cold empathy. This is an oxymoron, as the two concepts are contradictory and incongruous. Coldness implies detachment from feelings of others. Empathy implies responsiveness to feelings of others. Grudging respect is possible. Respect i based on cognitive judgment rather than feelings.

Definition of empathy from Oxford Dictionaries online:

The ability to understand and share the feelings of another.

Definition #5 of cold from Merriam Webster Learner's Dictionary:

not friendly or emotional,not friendly or emotional, lacking emotional warmth

Why is he so cold and distant toward me?

Example sentences:

She gave me a cold stare and turned away.

I got a cold reception when I came home.