Thermal losses from the hot end to the cold end of a Stirling cycle regenerator due to thermal dispersion through the regenerator matrix may significantly degrade the performance of the machine. Because of poor access to the void spaces within the porous medium, no direct measurements of thermal dispersion have been made and dispersion models have been derived indirectly by measuring the overall thermal performance of the regenerator while subtracting off the energy transfer caused by molecular conduction and advected enthalpy flows as computed from volume-averaged fluid velocity and temperature. In the current program, a large-scale porous matrix consisting of stacked screens with a porosity of 90% is installed in a flow rig which is operated in a dynamically similar fashion to that of a Stirling engine regenerator flow. Experiments are conducted to measure turbulent transport of momentum at the exit plane using hot-wires. Future measurements with resistance thermometry will add turbulent transport of thermal energy. Such turbulent transport terms are related to the thermal dispersion term in the volumetric-averaged energy equation for the regenerator matrix. A dispersion model based upon the measurements is proposed and compared with a model deduced from previous measurements of jet spreading in the same matrix and with results of models documented in the literature. The test program is ongoing. The present paper reports on the test program and the experimental results to-date.