This paper deals with two-dimensional coupled thermoelastic problems under the assumption of state of plane strain. The method uses the Laplace transform, taken over the temporal variable, along with the separation-of-variables technique. The general solution is obtained in the transform domain without introducing thermoelastic potentials (direct approach). As an application, the Lamb plane problem is investigated for two different loading conditions. The steady-state (large times) temperature solution obtained in this investigation is in full agreement with that obtained by a previously published different method.