We present an approximate theoretical treatment of pressure and viscous heating effects on the flow of a power law fluid through a slit die. It is assumed that the flow remains one dimensional, and the accuracy of this approximation is checked via finite element simulations of the complete momentum and energy equations. For pressures typically achieved in the laboratory it is seen that the one dimensional approximation compares well with the simulations. The model therefore offers a method of including pressure and viscous heating effects in the analysis of experiments and is used to rationalize experimentally obtained pressure profiles for the flow of polymer melts through a slit die. Data for the flow of a linear low density polyethylene and a polystyrene melt in a slit die show these two effects are significant under normal laboratory conditions. Thus, the shear stress-shear rate curves will be affected to the point of being inaccurate at high shear rates. In addition, it is found that the typical technique to correct for a pressure dependent viscosity is also inaccurate being affected by the viscous heating and heat transfer from the melt to the die.