A theoretical solution is presented of a problem of transient heat conduction in a one-dimensional three-layer composite slab. A full series solution for impulsive heating is found by employing a 'natural' orthogonal relationship between the eigenfunctions. The eigenfunction expansion solution is compared with a finite difference numerical solution. Based on a previous analysis of the two-layer problem, and the present three-layer problem, a conjectured partial solution for an n-layer composite slab is given. (C) 2003 Elsevier Ltd. All rights reserved.