Diamine-appended metal-organic frameworks exhibiting step-shaped CO2 adsorption are exceptional candidates for energy-efficient carbon capture. However, there are few studies examining their performance in real-world capture scenarios, in part due to the challenge inherent in modeling their CO2 uptake behavior. Here, we develop a dual-site Sips model to fit experimental CO2 adsorption data for dmpn-Mg2(dobpdc) (dmpn = 2,2-dimethyl-1,3-diaminopropane; dobpdc4- = 4,4′-dioxidobiphenyl-3,3′-dicarboxylate) and develop a linear driving force model for the adsorption kinetics based on available experimental data. These models are used to develop a dynamic, fixed bed, nonisothermal contactor model using shaped particles of the material, which is validated with experimental breakthrough data. We also examine the effects of the high heat of adsorption of the material on CO2 uptake performance and find that heat removal is essential to maximize capture performance. We finally investigate "basic"(no bed cooling during adsorption) and "modified"(bed cooling during adsorption) temperature swing adsorption (TSA) processes using dmpn-Mg2(dobpdc), and their process economics are compared to a state-of-the-art monoethanolamine (MEA) capture system with and without heat recovery. In the absence of heat recovery, the adsorbent systems are more costly than established technology. However, with 85% heat recovery, both adsorbent-based TSA processes are projected to cost less than the MEA system. This work highlights that thermal management is vital for implementation of dmpn-Mg2(dobpdc) as a viable CO2 capture technology. Investigation of other contactor technologies that can provide unique ways to manage system heat represent promising future areas of study.