We report the results of measurements of the grain size distribution function and the thermal conductivity of ultrafine-grained copper produced by equal channel angular pressing (ECAP), with special attention to the evolution of these quantities with the number of pressing cycles. To explain the experimental findings, the equilibrium grain size distribution function (GSDF) evolving during ECAP has been calculated on the basis of a simplified theoretical model. The model involves a single unknown physical parameter—the most probable grain size. With this parameter fitted to the experimental data the calculated GSDF fairly closely reproduces the experimental data. A model for thermal conductivity of ECAP processed copper has been proposed, which relates thermal conductivity to the GSDF parameters and the coefficient of electron reflection at grain boundaries.