Does renormalization group flow have to decrease temperature when $T<T_C$, with $T_C$ being critical point temperature? I think not, but my professor suggests something like that. Maybe I misunderstood him. I am asking whether temperature decrease has to happen along renormalization group flow in all reasonable circumstances, not just for specific circumstances.
What would happen for $T>T_C$? Would there be monotonic temperature increase or decrease in reasonable circumstances?