We measure and analyze the effective spin Hall angle of platinum in the low-residual resistivity regime by second-harmonic measurements of the spin-orbit torques for a multilayer of Pt vertical bar Co vertical bar AlOx. An angular-dependent study of the torques allows us to extract the effective spin Hall angle responsible for the damping-like torque in the system. We observe a strikingly nonmonotonic and reproducible temperature dependence of the torques. This behavior is compatible with recent theoretical predictions which include both intrinsic and extrinsic (impurities and phonons) contributions to the spin Hall effect at finite temperatures.