At the start of the feed step, thermal swing adsorption (TSA) processes generate a thermal pulse. This thermal pulse is generated by insufficient cooling of the bed during the regeneration step and bed repressurization following the cooling step. For some integrated processes, such as cryogenic air separation units (ASU), the thermal pulse generated by the TSA PPU (pre-purification unit) may not be acceptable. Three options are outlined to minimize the magnitude of the thermal pulse generated by the adsorbent bed during the feed step before the feed enters the equipment downstream of the adsorption process. A mathematical model to simulate this process and results from computer simulations are presented. Various process options are compared. Experimental data is compared against the model predictions.