A laundry drying appliance (100) includes a cabinet (110) having a top (119), a rotating drum (105) accommodated within the cabinet, and a laundry drying air circulation system for circulating drying air though the drum for drying laundry within the drum. The top includes fluid passageways defined thereinside for the circulation of the drying air, and an air-air heat exchanger (535) arranged inside the fluid passageways operable to remove moisture and dehydrate the drying air, a cooling air aspirator (560) for aspirating cooling air (555) from an external environment and causing the cooling air to flow through the air-air heat exchanger for cooling down the drying air and causing the moisture-laden air to condensate, and a perforated top panel (592;1805) having perforations for allowing release of the cooling air to the external environment after the cooling air has passed through the air-air heat exchanger. The perforated top panel defines a garments drying surface adapted to be laid upon by garments to be dried.