Similarity transformations are constructed and used to obtain an exact solution for the axisymmetric boundary value problem of an elastic half-space subjected to a continuous point heat source on its surface. It is found to agree with known results, obtained by Parcus with the help of the thermoelastic potential method. The temperature, displacements and stresses are used in the solution of the thermoelasticity contact problem with frictional heating for the ＇pin-on-half-space＇ tribosystem.