The invention relates to a plate-type heat exchanger for drying a gaseous medium, especially air, comprising a stack of plates which are interconnected to define flow spaces between the plates, a gas-gas heat exchanger being formed in one portion of the stack, with a moist inlet gas stream flowing away from an inlet gas connection and a dried outlet gas stream flowing towards an outlet gas connection, both flowing next to each other through separate flow spaces to exchange thermal energy, and a gas-coolant heat exchanger being formed in another portion of the stack, with a coolant and the moist inlet gas stream flowing next to each other through further separate flow spaces for cooling purposes, and a flow connection being formed between an outlet of the gas-coolant heat exchanger and the gas-gas heat exchanger, in-cluding an overflow member to guide the dried outlet gas stream through the overflow member from the gas-coolant heat exchanger to the gas-gas heat exchanger The overflow member is formed of a stack of adjacent plates which are interconnected to define overflow spaces between the adjacent plates, contact zones being established between side surfaces facing each other of the adjacent plates.