A cold storage heat exchanger includes a plurality of tubes, a coolant flowing in the tubes, a cold storage material container joined to the tubes, the cold storage material container defining a room that houses a cold storage material, and a distribution tank unit that distributes the coolant to the tubes. A coolant passage is formed in the tubes and the distribution tank unit. The distribution tank unit includes an aperture plate that reduces a passage cross-sectional area of the coolant passage. Among the plurality of tubes, the cold storage material container is joined to at least a tube disposed upstream in a coolant flow direction from the aperture plate in the coolant passage. Accordingly, cold storage performance may be improved.