For some reason I find her emotional coldness quite interesting!
That's exactly why I think Schizoids are quite often attractive people. My emotional spectrum (as in my internalised spectrum) is so narrow, that I never stress, I never freak out, get enraged, lash out or behave negatively towards anyone. I am calm in what others see as highly stressful situations. To others, I suppose I appear to be a highly confident, self-controlled pillar of stability, and people do find that attractive. Though when they make their feelings known to me, I have no choice but to turn them down. I could never be the man they need in a relationship, and it could never end well. But I have to do it in such a way that doesn't negatively reflect on myself (I have had to turn down several colleagues over the years for example, whilst maintaining my general persona and reputation). My usual response is 'I'm very flattered, but I don't date people I work with as it tends to get very complicated, and never usually ends well'. This has served me well enough. All of my so-called 'friends' are people I work with, so hopefully this should suffice for many years to come.
If someone from outside of work told me they liked me, there would be a choice for me to make. Do I be honest and answer as my schizoid self, or should I let my external persona deal with it in a way I think a normal person would. It's something I haven't really thought about before.