An outdoor unit for an air conditioner, and an air conditioner are provided that allow for effectively cooling a cooled part such as a power element, even when a refrigerant is not circulated, to prevent the part from being damaged by generated heat. Said outdoor unit and said air conditioner each include: a casing; a heat exchanger that exchanges heat between a refrigerant flowing therein and air; a blower fan that sucks air outside the casing and forces the air to pass through the heat exchanger; an electric parts box that has a board and a part to be cooled; and a cooling member that is thermally connected with said part and cools it with a refrigerant flowing therein, wherein the cooling member is arranged on an outer wall surface of the electric parts box in a path of the air blown by the blower fan.