The flow of polymer melts in cylindrical, annular, and slit dies has been examined. Large temperature rises at the outer surface of the extrudate were measured with an infrared pyrometer. Calculations show that severe radial temperature gradients exist in these flow geometries under conditions similar to those encontered in polymer processing and in viscometry measurements. A common method of estimating the average temperature rise from the total mechanical energy input seriously underestimates the maximum temperature rise. A numerical solution of the flow and energy equations models the flow in all three geometries. A very simple Nusselt number correlation allowed an estimate of the temperature rises possible if heat transfer with the die wall occurrs. Good agreement was obtained between predicted and infrared measured melt surface temperature rises. The pressure drop gives only an indication that nonisothermal flow is occuring and is not sensitive enough to distinguish the type of heat transfer boundary condition present. The mathematical model presented could be helpful in die design and in process modeling, allowing the designer to obtain some knowledge of the kind of flow situations which might be encountered.