The escalating energy demands in buildings, particularly for heating and cooling demands met by heat pumps, have placed a growing stress on energy resources. The bi-functional thermal diode tank (BTDT) is proposed as thermal energy storage to improve the heating and cooling performances of heat pumps in both summer and winter. The BTDT is an insulated water tank with a gravity heat pipe (GHP), which can harvest and store heat passively from sun radiation and the external environment during the daytime. In summer, it harvests and stores cold energy from the air and night sky during the daytime. The performance of the BTDT-assisted heat pump (BTDT-HP) system in Adelaide, Australia, during the 2021–2022 summer and winter seasons was evaluated by conducting a TRNSYS simulation. This study revealed that the BTDT-HP system outperformed the reference ASHP system, where up to 8% energy in heating and 39.75% energy in cooling could be saved. An overall reduction in the energy consumption of 18.89% was achieved. Increasing the BTDT volume and GHP panel area enabled the tank to store more thermal and cold energy across the winter and summer seasons, thereby improving the system’s performance. The maximum ESPs were found to be 31.6% and 41.2% for heating and cooling for the study case under optimal conditions. When the GHP panel area was fixed at 15 m2, the BTDT volume should be at least 28 m3 for the BTDT-HP system, boasting cooling and heating capacities of 40 kW and 43.2 kW, to achieve positive energy savings.