Paratransit is an essential mobility service legally mandated through the Americans with Disabilities Act (ADA). This type of service facilitates door-to-door shared rides for passengers with disabilities by utilizing a centrally coordinated trip scheduling and vehicle routing system. The vehicle scheduling problem in this context is a variant of the Pickup and Delivery Problem with Time Windows (PDPTW), which involves the scheduling of riders across multiple vehicles while satisfying the passenger timing constraints and vehicle capacities. Improving service efficiency helps paratransit providers reduce operating costs and maintain reliable service. The scheduling and routing must also be computationally tractable for practical reasons. We study a new approach for solving the paratransit scheduling problem using a temporal decomposition-based approach known as the Rolling Horizon Request-Trip-Vehicle assignment algorithm, which breaks down the complex PDPTW problem into smaller yet overlapping subproblems. The size of these subproblems is defined by a sliding window size, while the step size determines the number of subproblems. This study aims to comprehensively analyze the performance of this approach and how the two major tuning parameters impact the tradeoff between service rate and computation time. We assess the performance of this approach on a variant of a classical benchmark dataset for the PDPTW and showcase its benefits compared to a well-known alternative, LKH3.