Solutions for stress distributions in a flat plate with a circular opening which is undergoing radial and temporal changes in temperature are presented. A typical example would be a hot pipe penetrating a wall or a welding process. The problem is formulated as a partial differential equation on an infinite-domain problem with inhomogeneous boundary conditions. As such, the solution of the problem is obtained through integral-transform methods involving integrals difficult to numerically evaluate. The problem may also be formulated as a finite-domain problem with eigenvalue solution. The results in this case depend on the number of eigenvalues calculated which depends on the time value chosen. Three types of thermal boundary conditions are considered: (1) convection on the boundary, (2) insulated boundary, and (3) sudden heating or cooling, that is, thermal shock. Some sample results comparing the integral-transform and eigenvalue methods are presented. The results indicate that temperature values computed by both methods for an aluminum sample with a 1.5 in (0.0381 m) hole at time 10 s are identical to four decimal places. The finite domain outer radius for the eigenvalue solution was taken to be 18 in (0.4572 m). However, there is a discrepancy when comparing radial and tangential stress. This difference is the stress caused by the constant temperature from the finite boundary to infinity when imposed on the finite-domain problem.