A numerical investigation of heat transfer with viscoelastic fluid based on the FENE-P model in the entrance region of an axisymmetric pipe is carried out to analyze the influence of the rheological parameters on heat transfer enhancement with negligible axial heat conduction and viscous dissipation. Numerical simulation is conducted using the finite element based software Polyflow. The analysis considers a constant wall heat flux boundary condition and shows that an increase in fluid elasticity raised the normalized heat transfer coefficient due to the increased level of shear-thinning behaviour. But increasing the extensibility parameter L-2 leads to a decrease in Nusselt number.