The invention relates to a heat recuperator (R) for a radiating tube burner having a burner pipe and an exhaust pipe (1), the recuperator being placed at the outlet of the exhaust pipe (1) and including a heat exchanger (E) that comprises: an outgoing section (5) for directing the air to be preheated to a ferrule (6), placed on the end of the recuperator, from the fume intake side, and a return section (7) opening towards a pipe (8) for supplying air from the burner, the assembly being provided such that part of the fumes are led through, and mix with, the combustion air; the heat exchanger (E) occupies only part of the cross-section of the exhaust pipe (1), the other part (1a) of the cross-section remaining free for the fumes; the combustion air is heated by the fumes in the outgoing section (5) and in the return section (7), being radially shifted outside the outgoing section (5) and immersed in the fumes.