A two dimensional problem for an infinite thermoelastic half space is formulated, to study the thermoelastic response due to a periodically varying heat source within the context of Lord-Shulman theory. The bounding surface is traction free and subjected to a known temperature distribution. Integral transform technique is developed to find the analytic solution in the transform domain by using direct approach. Inversion of transforms is done employing a numerical scheme. Mathematical model is prepared for Copper material and numerical results for temperature, displacements and stresses are obtained and illustrated graphically.