Exact solutions are given for the transient temperature in flux-base fins with the method of Green's functions (GF) in the form of infinite series for three different tip conditions. The speed of convergence is improved by replacing the steady part by a closed-form steady solution. For the insulated-tip case, a quasi-steady solution is presented. Numerical values are presented and the conditions under which the quasi-steady solution is accurate are determined. An experimental example is given for estimation of the heat transfer coefficient (HTC) on a non-rotating roller bearing, in which the outer bearing race is treated as a transient fin. (C) 2008 Elsevier Ltd. All rights reserved.