The relaxation time τ is nearly independent of applied E field whereas it changes significantly with temperature T. First fact is (in part) responsible for Ohm’s law whereas the second fact leads to variation of ρ with temperature. Elaborate why?
Relaxation time independent of electric field, as velocities show a rather slow variance with electric field, usually of the order 1mm/s. Thus, the drift velocity is not hugely affected.
But increasing temperature changes the velocities of electrons by a magnitude of 102 m/s. This directly affects the relaxation time (higher velocities means shorter relaxation times).