A dishwasher drying system includes an air inlet configured to receive hot, humid air from a tub of a dishwasher. The dishwasher drying system also includes an air outlet configured to discharge the air to an ambient environment outside the dishwasher. The dishwasher drying system further includes an air moving device configured to cause the air to move from the air inlet to the air outlet. In addition, the dishwasher drying system includes a thermal storage heat exchanger positioned within an airflow path of the moving air, the thermal storage heat exchanger configured to absorb heat and condense moisture from the moving air as the moving air contacts the thermal storage heat exchanger during a dishwasher drying cycle.