The physics of a wall-confined, fully ionized plasma is studied in the case where β ≫ 1. When electron thermal diffusion is magnetically reduced, but still dominates over ion diffusion (1 ≲ ωeτe ≲ (mi/me)¼), the Nernst effect is shown to increase the diffusion losses substantially. Simple criteria are derived to estimate the validity of the 'equipressure' condition. The results are checked by a onedimensional hydro-code including the complete magnetic-field evolution. These results depend strongly on the wall boundary condition for the magnetic field.