This study investigates the thermal behavior and moisture transport phenomena by capillary action of sustainable cementitious composites made with recycled wood aggregates filled with bio-based phase change materials, aiming to enhance energy efficiency and durability in building applications. Two numerical models are developed and validated: an enthalpy-based thermal model using the Apparent Calorific Capacity Method, and a moisture diffusion model based on Richards’ equation and extended Darcy’s law. Experimental data were obtained from three mortar types: i. ordinary Portland cement, ii. Wood mortar, and iii. a third type fabricated with PCM–RWA aggregates labeled as “NRG-WOOD”—and used to benchmark the simulations. The thermal model successfully captured latent heat storage and release during heating and cooling cycles, while the hygric model accurately predicted capillary water absorption across all mixes. Notably, the NRG-WOOD mortar exhibited significantly reduced water uptake (<5 kg/m2), attributed to modified pore structures induced by PCM encapsulation, as reflected in elevated Raleigh-Ritz parameters. Both models showed strong agreement with experimental results without requiring post-calibration, underscoring their robustness and predictive reliability. This dual functionality—enhanced thermal regulation and reduced moisture ingress—highlights the potential of PCM–RWA composites as sustainable, high-performance building materials.