A Rapid Cycle Adsorption Pump (RCAP) is a competitive technology for capturing and pressuring CO2 within a Martian In-Situ Resource Utilization (ISRU) system. In an ISRU plant, CO2 from the Martian atmosphere at ~0.69-0.925kPa must first be pressured to ~101-500kPa to produce O2 and/or CH4. A RCAP pressurizes CO2 by imposing fast temperature swings on an adsorbent bedlow pressure CO2 is adsorbed onto the cooled bed, and higher pressure CO2 is desorbed from the heated bed. To aid the design of a RCAP for NASA's Advanced Exploration Systems (AES) ISRU project, a finite difference thermal model of a single stack RCAP was developed in Thermal Desktop. The stack consists of one gas passage sandwiched between two sorbent beds and two cold plates (for heating/cooling each bed). The model implements adsorption/desorption physics via a linear driving force approximation in order to predict both temperature and pressure swings in the pump. The modeling approach is presented along with a discussion of its results and the current design. The model was also used to trade cooling speed when constructing the RCAP with 3D printed high thermal conductivity copper (GRCop-84) verses 3D printed aluminum (AlSi10mg). A wide assembly was modeled to predict the performance of multiple stacks in parallel. Major performance drivers were identified to be 1) the contact heat transfer to the sorbent bed, and 2) the pump's thermal mass.