Lebon-Lambermont's variational principle is used to solve some problems of unsteady heat conduction in semi-infinite solids. These are characterized by temperature dependent heat conductivity and heat capacity. Two kinds of boundary conditions are applied: prescribed temperature history and prescribed heat flux across the surface. This latter problem is investigated by means of the technique proposed by Lardner and Rafalski-Zyskowsky. The results are compared with exact ones, when available, or with those obtained from other variational principles like Biot's and Vujanovic's. In all cases, agreement is very satisfactory. © 1974, Noordhoff International Publishing. All rights reserved.