Heat transfer to viscoelastic fluids is frequently encountered in various industrial processing. In this investigation an analytical solution was obtained to predict the fully developed, steady and laminar heat transfer of viscoelastic fluids between parallel plates. One of the plates was stationary and was subjected to a constant heat flux. The other plate moved with constant velocity and was insulated. The simplified Phan-Thien-Tanner (SPTT) model, believed to be a more realistic model for viscoelastic fluids, was used to represent the theological behavior of the fluid. The energy equation was solved for a wide range of Brinkman number, dimensionless viscoelastic group, and dimensionless pressure drop. Results highlight the strong effects of these parameters on the heat transfer rate. (C) 2004 Elsevier Ltd. All rights reserved.