A thermal Reynolds-Eyring equation is derived for elastohydrodynamic lubrication of line contacts. A control volume approach is used to analyze the inlet region where back-flow occurs. Numerical results are obtained and used to develop a formula for the thermal and non-Newtonian (Ree-Eyring) film thickness reduction factor. Results for maximum temperatures and traction coefficients are also presented. The pressure dependence of lubricant thermal conductivity is found to significantly affect the maximum lubricant temperature.