Well you've nailed the reason for my question right on the head:
  It _is_ odd to consider empathy in terms of thinking. Yet, they
  have a relationship: Sociopathy is an extreme example that there
  is _some kind_ of relationship between empathy and thinking. But
  what kind? Is there a correlation to be found? Or do they run in
  parallel? How to describe their relationship? That's what I'm
  striving to figure out, if possible and why I'm asking for help.
  Perhaps they are axis on a 2D grid, with empathy running one way
  and thinking running the other way, and one can plot their
  relationship as it stands in a given situation. That's one
  possibility I can think of.