This work applies multi-objective optimization based on a genetic algorithm to design a wall-type heat recovery and ventilation (HRV) unit equipped with a phase change material (PCM) to show the benefits of using this thermal energy storage system in buildings. The initial design – taken from a reference work – consists of an airflow driven by a fan through a copper tube bundle filled with PCM. Starting from this, a thermo-fluid dynamic 3D model is developed to assess the natural convection negligibility inside the PCM. Then, a 2D model is solved with a commercial finite element code and validated. Once the validation is assessed, this model is coupled with MATLAB® to perform the multi-objective optimization procedure. Optimal system configurations (tube diameter, thickness, pitches) and operational variables (fan velocity, cycle time, PCM melt temperature) are achieved on a 3D Pareto surface that collects the non-dominated solutions, i.e., minimizing costs and pressure drop (air side), and maximizing the average storage rate. The 3D Pareto approach enables to find solutions that outperform the initial configuration, i.e., the average storage rate is increased by 28.4%, simultaneously improving the other two objective functions. Finally, two sub-optimal solutions from the 2D fronts are numerically compared to show the difference in the air stream distribution across the new tubes’ arrangement and the PCM melting evolution. The HRV efficiency is enhanced from 37.5% to 44.4%, confirming that the proposed approach provides an economically-feasible solution, while reducing energy consumption and maintaining good indoor air quality.