To provide a cold storage material container with high reliability capable of surely preventing leak of a cold storage material from the cold storage material container with a simple configuration, and a cold storage heat exchanger .

A cold storage heat exchanger (1) includes: a plurality of cooling medium circulating tube parts (2) in which a cooling medium flows; and a cold storage material container (4) in which a cold storage material cooled by the cooling medium flowing in the cooling medium circulating tube parts is sealed. The cold storage material container includes: a container body (16) which is arranged in the proximity of the cooling medium circulating tube parts; a sealing tube (18) of the cold storage material which is protrusively formed at one end side in a longitudinal direction of the container body and which communicates with the container body; and a lid member (20) which is inserted into the sealing tube. The sealing tube includes a reduced diameter part (32) in which an opening end wall (24) on the outer side than the lid member is reduced in diameter. The lid member includes a contact part (40) which is air-tightly abutted with the whole inner periphery of the opening end wall all along.