Interesting. Cold-heartedness is really a too pejorative term for it, I'd say. But I understand what you're talking about. I have similar problems. It's been associated with schizophrenia and autism spectrum disorders. There are two distinct types. Very different types but they appear quite the same.

It's not really a diagnosis of a mental disorder, more like a trait. I personally think it's an underlying and essential feature of disorders which are like BP, SZ and ASD, but as I said it's very likely there are two (very) different problems which may appear very similar.

It could also very well be there's no genetic component at all, but just a childhood with abuse and anxiety, as you described.

Do you have any problems in functioning? Do you have any other problems? How is your memory? Are you impulsive and do you easily get angry? Do you ever feel bored? Does it cause anger and frustration, lethargy or hopelessness? If so, you might want to make sure you don't have a personality disorder. Do you ever experience hallucinations or delusions, extreme changes in beliefs, the importance of thing and perception?

Edit:
Knowing whether you might have a personality disorder (and which) might help you understand others problems in functioned, some of which you might not have realised you had.