Carbon capture is one of the recently raised technologies to mitigate greenhouse gas emissions. Adsorption was introduced as an energy-efficient carbon capture process, and the literature primarily shows the utilization of circular cross-sectional adsorption beds for this purpose. In this regard, this paper investigates different shapes of adsorbent beds to determine the thermal and adsorption uptake enhancements. Three geometries are considered: circular, square, and triangular cross-sectional beds. Mg-MOF-74 is used as an adsorbent, and numerical simulation is developed using a user-defined function coupled with ANSYS-Fluent. The results show that the triangular cross-sectional bed exhibits better adsorption capacity and thermal management compared to other beds. For example, the triangular cross-sectional bed shows 6 K less than the circular one during the adsorption process. It is recommended that the triangular cross-sectional bed be used for temperature swing adsorption when pumping power is not important. The square bed comes second after the triangular one with a lower pressure drop, suggesting such beds as good candidates for pressure swing adsorption. The square bed could be an excellent choice for compact beds when CO2 uptake and pumping power are both important.