  Thermal measurements on a GaAs/AlGaAs heterostructure reveal that the state
of the confined two-dimensional electrons dramatically affects the nuclear-spin
diffusion near Landau level filling factor \nu=1. The experiments provide
quantitative evidence that the sharp peak in the temperature dependence of heat
capacity near \nu=1 is due to an enhanced nuclear-spin diffusion from the GaAs
quantum wells into the AlGaAs barriers. We discuss the physical origin of this
enhancement in terms the possible Skyrme solid-liquid phase transition.
