The frequency response behaviour of the adsorbent temperature is analysed in detail for both diffusion in crystals and in biporous pellets. In the case of crystals, it is shown that the temperature frequency response may exhibit very different behaviour under effects of intracrystalline diffusion or surface barrier, making it easier to discriminate between the diffusion and surface barrier processes. For biporous pellets, the frequency response of the surface temperature proves to be very sensitive to the competition between micropore diffusion and macropore diffusion, due to finite-rate heat conduction inside pellets. This high sensitivity can lead to a much better estimation of the micropore diffusion coefficient in the presence of macropore diffusion than the estimation obtained with the gas pressure frequency response. Finally, it is shown that, in the case of high-pressure experiments, the effect of heating by gas compression may be significant if the gaseous adsorbate has a large specific heat ratio and a large heat capacity, and if the heat exchange at the chamber wall is slow enough. The effect of gas compression heating on the temperature frequency response is confirmed experimentally for diffusion of xenon in zeolite 5A crystals. The present paper shows, however, the effect of gas compression heating on the gas pressure can be efficiently eliminated using the frequency response data corrected with respect to blank experiments, as proposed by Yasuda.