A dishwasher appliance is provided. The dishwasher appliance includes a cabinet and a tub positioned within the cabinet. The tub may define a wash chamber. The dishwasher appliance may also include a drying system comprising a cooling conduit, a first fan, and a second fan. The cooling conduit may define a cooling conduit passage that is in fluid communication with the wash chamber. The first fan may be operable to draw wash chamber air into the cooling conduit passage. In addition, the second fan may be operable to direct a flow of ambient air onto an exterior surface of the cooling conduit.