This paper considers a transient heat conduction problem for all infinite medium with two non-overlapping circular cavities. Suddenly applied, steady Dirichlet type boundary conditions are assumed. The approach is based on superposition and the use of the general solution to the problem of a single cavity. Application of the Laplace transform results in a semi-analytical solution for the temperature in the form of a truncated Fourier series. The large-time asymptotic formulae for the solution are obtained by using the analytical solution in the Laplace domain. The method can be extended to problems with multiple cavities and inhomogeneities. (c) 2007 Elsevier Ltd. All rights reserved.