Creating a module that achieves sustainable CO2 capture while being compatible with the existing industry is paramount in overcoming the current CO2-driven environmental issues. This paper presents the fabrication of hollow fiber sorbents (HFSs) and their respective modules to capture CO2 by the rapid thermal swing adsorption process (RTSA). Poly(amide-imide) (PAI)/microspheric SiO2 composites were fabricated with a so-called "sieve-in-a-cage" microarchitecture which promotes CO2 diffusion. More importantly, a selected amount of 1,2-epoxybutane (EB)-functionalized poly(ethylenimine) (PEI), denoted as 0.37EB-PEI, was incorporated into our PAI/SiO2 composites forming PAI/SiO2/0.37EB-PEI HFSs which enhanced the thermal stability with a moderate CO2 sorption uptake of 0.88 mmol CO2 g(-1). The resulting HFSs were assembled into a module using either stainless steel (SS) or poly(tetrafluoroethylene) (PTFE), and their respective CO2-capturing performances in the RTSA process were compared. The two modules had a comparable breakthrough CO2 capacity of 0.42 mmol CO2 g(-1) for a wet feed mixture of CO2/He/N-2 (14 mol/14 mol/72 mol) (RH 100%) and a comparable CO2 desorption efficiency (i.e., 95% desorption within 2 min) under 100% CO2 at 120 degrees C due to the presence of the 0.37EB-PEI; however, different thermal properties inherent to the modular materials caused the PTFE-based module to outperform the SS-based counterpart in terms of cooling, enabling the execution of an entire RTSA cycle within 8 min. Additionally, the PAI/SiO2/0.37EB-PEI/PTFE module maintained its breakthrough capacity of 0.42 mmol CO2 g(-1) over five consecutive RTSA cycles, confirming its good long-term stability as well.