The general solution for the stress and temperature distribution in an isotropic thermoelastic solid occupying the half space has been given when the classical heat conduction equation is suitably modified to take into account the effect of variation of strain on the variation of temperature, the boundary of the solid being assumed to be stress-free but with prescribed temperature distribution. As an illustration the axial temperature distribution in a particular metal has been found for small values of time. The method of integral transform is used as the mathematical tool.