Heat storage unit having at least one storage block which is designed as a bundle of a plurality of closed hollow chambers made from hollow profiles, which chambers extend in parallel with one another, extend longitudinally in the z-direction, and are each filled with PCM material, - in the cross-sectional plane extended in the x-y direction, both in the x-direction and in the y-direction of the storage block, at least two hollow chambers having wall portions (a, b, c, d) of their peripheral walls being arranged so as to closely abut one another directly over the surface or indirectly via a thin, highly thermally conductive contact layer, - the peripheral walls being provided with indentations extending over their entire length in the longitudinal direction at least in some of their wall portions (a, b) which are opposite one another in pairs, - the indentations in the peripheral walls of two adjacent hollow chambers complementing one another in cross-section to form a closed, in particular circular, ring, and - a line arrangement being guided through the storage block so as to convey heat-transporting fluid, which line arrangement has at least one line comprising a plurality of line portions, which are connected in the indentations in direct contact or in contact established via a heat-conducting means to each of the adjoining regions of the peripheral wall and to the PCM material thereon, characterized in that the wall portions (a, b) opposite one another in pairs are provided with respect to only one arrangement direction (x or y) with a retaining element arrangement over their entire length, which arrangement has, in one wall portion (a), a hook-in groove having a groove recess, groove opening and retaining edge and, in the other wall portion (b), a retaining projection which can be inserted laterally into the hook-in groove at right angles to the z-direction and has a projection part and a retaining lug, which engages behind the retaining edge in the assembled state, it being possible for the hook-in groove and the retaining projection to be shaped and dimensioned in such a way that they can be fitted into one another in the arrangement direction (x or y) and to such an extent that the wall portions (a, b) opposite one another in pairs come into contact with one another directly or indirectly via the contact layer which may be located therebetween. - in the cross-sectional plane extended in the x-y direction, both in the x-direction and in the y-direction of the storage block, at least two hollow chambers having wall portions (a, b, c, d) of their peripheral walls being arranged so as to closely abut one another directly over the surface or indirectly via a thin, highly thermally conductive contact layer, - the peripheral walls being provided with indentations extending over their entire length in the longitudinal direction at least in some of their wall portions (a, b) which are opposite one another in pairs, - the indentations in the peripheral walls of two adjacent hollow chambers complementing one another in cross-section to form a closed, in particular circular, ring, and - a line arrangement being guided through the storage block so as to convey heat-transporting fluid, which line arrangement has at least one line comprising a plurality of line portions, which are connected in the indentations in direct contact or in contact established via a heat-conducting means to each of the adjoining regions of the peripheral wall and to the PCM material thereon,