Thank you!
As a technique, there is so-called Matsubara frequency calculation using something like imaginary temperature (not exactly, but it is the closest thing I can think about).
From the physical point of view, the imaginary temperature would mean complex probabilities, which is a very strange thing. From a frequentist approach, they do not make sense at all. From bayesian approach, we potentially can define it, but still not clear what would they mean.
Ok, but what would negative probability then be?