A model for the unsteady thermal boundary-layer development at the end wall of a shock tube, in partially ionized atmospheric argon, is proposed. Consideration is given to ionization and thermal relaxation processes. In order to obtain some insight into the influence of the relaxation processes on the structure of the boundary layer, a study of the frozen and equilibrium limits has been carried out. The transition from a near-equilibrium situation in the outer part of the boundary layer towards a frozen situation near the wall has been determined numerically. Experimental data on the electron and atom density profiles obtained from laser schlieren and absorption measurements are presented. A quantitative agreement between theory and experiment is found for a moderate degree of ionization (3 %). At a higher degree of ionization the structure of the boundary layer is dominated by the influence of radiation cooling, which has been neglected in the model.