We report on the temperature dependence of the recently discovered spin Hall magnetoresistance in a yttrium iron garnet (YIG)/platinum (Pt) thin film. The YIG/Pt layers are an ideal choice as the combination of an insulating magnetic material and the high spin-orbit interaction in Pt gives a relatively large magnetoresistance and no electrical conduction occurs in the YIG. The temperature dependence of the magnetoresistance was measured between 1.4 K and 280 K from which the temperature dependence of the spin diffusion length in Pt has been extracted. We found that the best agreement between our data and the recently published [Chen et al., Phys. Rev. B 87, 144411 (2013)] theory of the spin Hall magnetoresistance is given by an assumed Elliot-Yafet mechanism of spin relaxation with temperature-independent spin Hall angle and spin mixing conductance. The best estimate for the spin diffusion length returns values between 0.57 and 3.85 nm.