The present paper deals with the boundary layer flow and heat transfer of a non-Newtonian fluid at an exponentially stretching permeable surface. The Casson fluid model is used to characterize the non-Newtonian fluid behavior, due to its various practical applications. With the help of similarity transformations the governing partial differential equations corresponding to the continuity, momentum, and energy equations are converted into nonlinear ordinary differential equations, and numerical solutions to these equations are obtained. Furthermore, in some specific parameter regimes, analytical solutions are found. It is observed that the effect of increasing values of the Casson parameter is to decrease the velocity field while enhancing the temperature field. Furthermore, it is observed that the effect of the increasing values of the suction parameter is to increase the skin-friction coefficient.