For small temperature changes the resistivity varies linearly with temperature:

r = r_o (1 + a DT), where a is the temperature coefficient of resistivity.

We often write this in terms of resistance instead: R = R_o (1 + a DT)

In some materials (like silicon) the temperature coefficient of resistivity is negative, meaning the resistance goes down as temperature increases. In such materials an increase in temperature can free more charge carriers, which would be associated with an increase in current.