The differential diffusivity equation for an infinitely long cylindrical source with a constant heat flow rate in a homogeneous and isotropic medium has a solution in complex integral form. This integral cannot be expressed in terms of known functions. At present the temperature at the wall of the cylindrical source is determined by means of numerical integration techniques. However, in many cases the heat flow rate varies with time. In these cases the principle of superposition should be used, thus requiring an analytical solution for the constant heat flow rate case. In this paper we present a semi- analytical equation that can be used to approximate the transient dimensionless wall temperature. The accuracy of the equation proposed is also given. (C) 2002 CNR. Published by Elsevier Science Ltd. All rights reserved.