A Real-time Operating System (RTOS) manages the execution order of tasks with a scheduling algorithm to meet timing requirements. The scheduler frequently checks for ready tasks during context-switching. However, high task numbers can cause longer processing time in this routine. RTOSs are mainly implemented in software, but reconfigurable computing enables offloading to reduce, e.g., the processing time of context-switching. On the other hand, optimizing the energy efficiency of running applications is desirable. Power-saving techniques allow adapting current dissipation to required operating conditions. However, unplanned use can lead to missed deadlines in real-time applications. Therefore, real-time capability and energy efficiency have to be appropriately balanced. This work explores the impact of power-saving techniques on real-time requirements while supporting RTOS with offloading methodologies. A mapping strategy assigns tasks to Processing Elements (PEs) based on task dependency, inter-task/processor communication, and power consumption metrics. A multi-core architecture is designed with a Network-on-Chip (NoC) and four PEs in a 2D-mesh topology. The master PE manages the system architecture, executes the mapping strategy, and dynamically scales voltage to reduce power consumption while running an RTOS. The task scheduling is offloaded to the co-processor. On the other hand, each slave PE executes assigned tasks with an RTOS and performs an inter-task/processor communication. The task scheduling here runs on the reconfigurable hardware. Each slave PE locally adapts power with frequency scaling and clock gating. The experimental results show that co-processor offloading reduces scheduling overhead by 26.58%, and hardware offloading reduces it by 33.33%. Additionally, the proposed solution has reduced overall power by 47.27% and energy consumption by 89.47%.