Disclaimer: I'm a physicist but have no expertise in solid state physics. I remember when the whole high-Tc thing started. My recollection is that the discovery broke what was at the time considered to be the mainstream understanding of superconductivity. And, a more comprehensive and satisfactory theory has not yet emerged. As a result, we're in a sort of tortoise-and-hare race between theory and experiment, where each one advances a bit when the other one catches up and makes a new discovery.
Disclaimer: I'm (technically) an engineer, not a physicist, but I took a course on this back in uni, and as far as I can remember, you're correct. The gist of it is that BCS theory, which satisfactorily explains conventional superconductivity, fails to predict the behaviour of high-temperature superconductors, and there simply isn't a better model available at the moment.
For any sane individuals reading this, the answer is "We're trying really hard but so far we haven't been able to deduce a formula for the highest temperature."
I'm not very optimistic with regards to this ever happening. I remember reading a paper regarding one of the many high-temperature superconductors, BSCCO; it has a crazy crystaline structure, it's quite unlikely that we'll ever come up with an analytical model describing its superconductive behaviour.
>we're in a sort of tortoise-and-hare race between theory and experiment, where each one advances a bit when the other one catches up and makes a new discovery.