A numerical investigation of heat transfer with viscoelastic FENE-P fluid in circular and non-circular ducts is carried out to study the effect of the solvent contribution on heat transfer in the absence of viscous dissipation by assuming temperature-independent model parameters. The numerical simulation is conducted using the finite element software POLYFLOW and results are compared with analytical and semi-analytical solutions available in the literature for the 20 axisymmetric pipes. 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 behavior. However, increasing the extensibility parameter L-2 leads to a decrease in Nusselt number. Local and average Nusselt number values are obtained for the axisymmetric pipe flows for several values of polymer concentration and the study confirms quantitatively that polymer concentration enhances heat transfer rates in FENE-P fluids. Nusselt number distribution in the fully developed region of tubes of equilateral triangular, square and rectangular cross-sections is reported for the first time for non-linear viscoelastic fluids of the FENE-P type with solvent contribution. (C) 2014 Elsevier B.V. All rights reserved.