A heat conduction problem is set up which, in essence, simulates the conditions arising when a plane shock wave reflects from a co-planar solid boundary. The gas is assumed to be polyatomic, with one 'significantly relaxing' internal energy mode. The quantity of primary interest is the temperature of the solid at the interface, since this can be observed experimentally without much difficulty. Solutions are obtained for this quantity which cover a range of practically plausible relaxation times and 'wall effect' parameters. It is essential to include proper temperature jump boundary conditions for both active and relaxing (or inert) energy modes. Thus it is necessary to know accommodation coefficients for these modes of energy storage. The temperature jump effects are found to dominate the (interface) solid's temperature/ time history, with relaxation effects playing a very secondary role. The theoretical results are compared with some experimental observations and encouraging agreement is found. As a result of this agreement it proves possible to estimate the accommodation coefficient for the active modes (in this case for the combination platinum/air), the pressure being about 15 atmospheres. The pressure sensitivity of accommodation effects is commented on.