A new finite integral transform method [Int. J. Heat Mass Transfer 44 (2001) 3307] is applied to the wave model of conduction. It is compared with a standard method of solution of the hyperbolic conduction equation. The temperature fields coincide. The chosen test problem and its results bring to the foreground some of the difficulties of standard technique applications. These difficulties are by-passed when using the new method. The Cattaneo Vernotte model is then tested through a comparison of its results with transient molecular dynamics simulations taken from Volz [Transferts de chaleur aux temps ultra-courts par la technique de la dynamique moleculaire, These, Univ. de Poitiers, 1996]. When the used parameters of the continuous model are near their equilibrium values, the agreement remains weakly qualitative. An adaptation of these parameter values, notably the diffusion time scale, can give a quantitative coincidence; but never is the agreement obtained for both studied variables (internal energy and flux density). These observations are discussed. Various causes liable to justify the realized adaptations of parameters are considered. None of them gives a right explanation. Concerning the impossibility of making both variables coincide, the source of conflicts is as much in the constitutive law as in the energy conservation law. The key seems to be in thermodynamics. (C) 2003 Elsevier Ltd. All rights reserved.