The invention relates to a ventilation assembly for a building, comprising a heat exchanger for bunging inbound ventilating air and outbound ventilating air in heat exchanging contact with each other, and provided with PCM material, an air displacement device for setting ventilating air into motion, a control device, functionally coupled to the heat exchanger and the air displacement device, for putting the ventilation assembly in:- a first setting in which inbound ventilating air has a first air supply flow rate, outbound ventilating air has a first air discharge flow rate, the inbound and outbound ventilating air are brought into heat exchanging contact with each other in the heat exchanger at least partially over the PCM material, and- a second setting in which inbound ventilating air has a second air supply flow rate and in the heat exchanger is substantially in heat exchanging contact with the PCM material, wherein inbound and outbound ventilating air are not in heat exchanging contact in the heat exchanger, and wherein the second air supply flow rate exceeds the minimum requirement of ventilation flow rate for creating extra cooling.
