The solution of thermal entry problem for pipe and channel flow of highly viscous liquids having viscoelastic properties, here modeled by the FENE-P constitutive equation, is obtained semi-analytically. Two types of boundary condition are considered, either an imposed wall temperature or a prescribed wall heat flux, and the effects of viscous dissipation are also taken into account. The analysis leads to a Sturm-Liouville problem similar to that found for the simplified Phan-Thien-Tanner fluid with linear stress coefficient, provided an adequate transformation of constitutive variables is performed first. The way to do this is explained and representative results for thermal entry flow of the FENE-P fluid are given. (C) 2004 Elsevier B.V. All rights reserved.