A drying appliance includes a cabinet. A blower directs process air through a closed-loop airflow path and through a processing chamber and a condensing unit. The condensing unit is attached to an external surface of the cabinet. An open airflow path directs ambient air through the condensing unit and to an area exterior to the cabinet. The ambient air remains separated from the closed-loop airflow path. The condensing unit is configured to exchange heat between the process air within the closed-loop airflow path and the ambient air moved through the open airflow path. The ambient air cools and dehumidifies the process air to form condensate on an interior surface of the condensing unit.