The time—space finite element method has been applied to one-dimensional non-steady heat conduction problems. By theoretical analyses based on the condition number of the relevant coefficient matrix, the time—space method has been found to be much more precise and stable than the Crank—Nicolson method. This has also been confirmed by several numerical analyses including the thermal problems of the first wall. As an application of the time—space finite element heat conduction analysis, the thermal ratchetting of the first wall has been analysed. By comparing the numerical results with the provisions of the ASME Code Case N-47, it has been found that N-47 cannot be applied to the thermal ratchetting of the first wall subjected to repeated plasma disruption.