Heat transfer through a porous medium can be significantly increased due to thermal dispersion. In the application of a Stirling regenerator, it may degrade the performance of a Stirling cycle machine due to thermal losses from the hot to the cold end of the regenerator. In the current program, a porous matrix consisting of stacked wire screens with a porosity of 90% is constructed and operated at Reynolds numbers that simulate flows in Stirling engine regenerators. Two experiments are conducted to determine thermal dispersion through the porous medium. One is to measure instantaneous velocity and temperature fields in the regenerator matrix exit flow under oscillatory flow conditions. Turbulent thermal energy transport quantities are calculated and a model for determining streamwise thermal eddy dispersion is developed. In the second experiment, temperature fields of a thermal wake downstream of a heated line source are measured within the porous medium. The thermal cross-stream dispersion is calculated indirectly by matching the measured temperature profiles to those predicted by the solution of the macroscopic energy equation with the thermal dispersion coefficient included as a parameter. The values of cross-stream dispersion found by indirect measurement are compared to values of cross-stream dispersion found by direct measurements, which are documented in the literature. The measured results are compared with computed results from a 3-D, CFD model composed of six cylinders in cross flow and in a staggered arrangement, which matches the dimensions and porosity of the porous matrix used in the experiments. The commercial code FLUENT is used to obtain flow and thermal fields. The effective thermal conductivities for the fluid (including thermal dispersion) are computed from the CFD results. These are compared to the indirect and direct measurement values.