Analyzing the effects of temperature variability on the operation of spintronic devices is of great importance for memory applications. This is because temperature variations often induce variations in the switching metrics such as the critical current density and write energy. Traditionally, predictive analysis of the effect of temperature variations was done using a Monte Carlo framework. In this paper, a far more numerically efficient surrogate modeling approach based on the Polynomial Chaos (PC) technique is presented for thermal analysis of spin-orbit torque (SOT) based magnetic random access memory (MRAM). Importantly, for a wide range of temperature variation from -50˚C to 120˚C, it has been demonstrated that the PC technique is able to predict the statistical variations of current density (JSOT) and write energy (Ewrite) with more than 99.9% accuracy while offering between one to three orders of magnitude in speedup over the conventional Monte Carlo framework.