The present invention relates to a tube (1) with a reservoir of phase-change material for a heat exchange bundle (100) of a heat exchanger, said tube (1) with a reservoir of phase-change material including: two flow plates (3) which are configured to be assembled with one another in a fluid-tight fashion and form at least one duct (31) in which a first heat-transfer fluid flows between said flow plates (3), at least one reservoir plate (5) including cavities (51), said reservoir plate (5) being configured so that it can be assembled in fluid-tight fashion on an external face of one of the two flow plates (3) so as to close the cavities (51) and form housings for the phase-change material, said cavities (51) projecting from the external face of the reservoir plate (5) so that that a second heat-transfer fluid can circulate between said cavities (51).