This paper concerns an axisymmetric dynamic treatment of a three-dimensional thermoelastic problem in a thick plate that is exposed to the temperature of surrounding medium depending on the position and time. In the present investigation, the Laplace transform and the convolution theorem are used, and an exact solution that is valid for the whole time interval without approximation is obtained. The thermal stresses are compared with the corresponding quasi-static stresses and the corresponding one-dimensional stresses.