The design of thermoacoustic coolers involves an adequate modeling of the thermoacoustic core's performance, which requires, in particular, a precise knowledge of their thermo-physical properties. Materials such as wire mesh stacks, foams, or compressed fibrous media are hard to describe, and their thermo-physical properties are rarely well enough quantified. Moreover, the classical linear thermoacoustic theory is not sufficient to accurately describe the performance of these materials. This paper deals with the experimental performance characterization of various materials for thermoacoustic heat pumping. A dedicated experimental test-bench has been specially developed, which is composed of two loudspeakers placed at opposite ends of a waveguide containing the porous material and a feedback loop to control the acoustic field in the porous material. Its originality is attributable to the possibility of identifying the optimal acoustic field, specific to each material, that maximizes the temperature difference at the ends of the material. Moreover, a specific protocol is implemented to access and compare the thermoacoustic heat flux through various materials at these optimal acoustic fields. Comparison of the experimental and theoretical results shows a reasonable agreement.