The present paper aims to study the transient thermal analysis of longitudinal fins with variable cross section considering internal heat generation. The profile shapes of the fins are considered rectangular, convex, triangular and concave. It is assumed that both thermal conductivity and internal heat generation are as linear functions of temperature. The power-law temperature-dependent model is used to simulate different types of heat transfer such as laminar film boiling, natural convection, nucleate boiling and radiation. The governing equation is derived as a nonlinear partial differential equation (PDE) that is solved using a hybrid approximate technique based on the differential transform method (DTM) and finite difference method (FDM). The results are presented to study the effects of some physical parameters such as fin profile shape, thermal conductivity, convection heat transfer coefficient and internal heat generation. (C) 2014 Elsevier Ltd. All rights reserved.