A magnetocaloric thermal apparatus (1) with a structure that rotates about a longitudinal axis (L), comprising a magnetic arrangement that defines at least two air gaps (E1, E2) parallel to each other and configured to create, in each of the air gaps, a magnetic field variable about the longitudinal axis (L). Two supports (S1, S2) carry magnetocaloric elements (2) and are positioned each in the midplane (P1, P2) of one of the air gaps. The magnetic arrangement and the supports are in relative movement with respect to one another and positioned angularly with respect to one another about the longitudinal axis (L) so as to generate a phase shift between the magnetic cycle undergone by the magnetocaloric elements (2) of one of the supports (S1) in one of the air gaps and the magnetic cycle undergone by the magnetocaloric elements of the other support (S2) in the other air gap.