The pressure responsep1of a fixed quantity of4Hegas subjected to sinusoidal volume perturbations is studied experimentally. Thermal diffusion near solid boundaries causes the gas response to be neither adiabatic nor isothermal. The data are interpreted in terms of the thermal relaxation functionfκwhich relatesp1to the spatial average of the acoustic temperature profile. Comparison of a number of geometries allows us to accurately determinefκfor a thermoacoustic pin-array stack.