The evolution of a temperature gradient at the free surface of a coating solution during the spin coating process is examined. Solvent evaporation causes localized cooling at the top that can result in thermocapillary instability within the coating solution, and thereby driving convective flows that may result in non-uniform coatings. We examine the evolution of these temperature gradients by using a one dimensional finite difference model that simultaneously describes the thinning behavior (both by flow and by evaporation) and the temperature evolution within the solution. The entire system is initially isothermal but is subject to evaporation-driven cooling at the free surface of the gradually thinning fluid. The model is then used to determine the magnitude of the thermocapillary effects during the spin coating process. As test systems we simulate the spin coating of several pure alcohol solutions having different volatilities and therefore different evaporative-cooling powers. As the fluid thins, we calculate the instantaneous Marangoni (Mn) number, which signifies the magnitude of thermocapillary-driven convection. We compare these Mn values against their relevant threshold values, determined from prior reports in the literature, in order to deduce the magnitude of the instabilities they represent. If the Mn value is super-critical, then the instability that it represents will be sufficient for the onset of convection cells within a stagnant fluid layer of corresponding thickness. Because the radial outflow is fully laminar under normal conditions, super-critical Mn values imply that similar instabilities would arise within a spinning solution. Super-critical Mn values were observed under numerous conditions suggesting that thermocapillary instability may be responsible for striation features that develop in coatings made by spin coating. Trends related to spin-speed, solvent volatility, and initial solution thickness are discussed with the goal of improving the flatness of coatings that are made by this process.