If, on the other hand, you would call a lottery in which you know the winning numbers "unfair", you should be equally willing to call water about which you know everything "cold".

In the lottery, there is something I can do with foreknowledge of the numbers: bet on them. And with perfect knowledge of the microstate I can play Maxwell's demon to separate hot from cold. But still, I can predict from the microstate all of the phenomena of thermodynamics, and assign temperatures to all microstates that are close to equipartition (which I am guessing to be almost all of them). These temperatures will be the same as the temperatures assigned by someone ignorant of the microstate. This assignation of temperature is independent of the observer's knowledge of the microstate.