Plastics can build-up on the die lip during extrusion. This phenomenon is called die drool and can be costly for plastics producers, requiring periodic shutdowns for die cleaning. Die drool has been attributed to the cohesive fracture of the melt into a drool layer and a bulk layer. The bulk layer slips on the drool layer after fracture, resulting in heating at the slip interface, called slip heating. The heat generated through slip heating can contribute to polymer thermal degradation, and to the die drool degradation. The impact of slip heating on die temperature rise has been investigated by neglecting viscous dissipation (Gilbert and Giacomin, 2014). This work considers viscous dissipation and its importance to slip heating. We find that viscous dissipation and slip heating contribute equally to the melt temperature rise, and we conclude with a worked example showing the importance of these two heating sources during polymer processing. We also develop two sufficient conditions for the accurate use of our results, Pe << 1 and partial derivative Theta/partial derivative zeta << partial derivative(2)Theta/partial derivative zeta(2).