Question

how does one explain increase in resistivity of metal with increase temperature?

Answer 1

With increase in temperature, the relaxation time (average time between successive collisions) decreases and hence resistivity increases.
Alternatively,

Answer 2

Hey !!

With increase in temperature, the relaxation time (average time between successive collisions) decreases and hence resistivity increases.

ALTERNATIVELY,

Resistivity, ρ = (m / ne²τ) increases as τ decreases with increase in temperature.

Good luck !!