The windbox burner has a register casing (2) with ports (3) for inflow of combustion air, a secondary air pipe (35) enclosed by the register casing and having inlet ports (36) for secondary air, a ring damper (20) coaxial with the register casing and axially displaceable and having at each end an annular sealing means (21; 26) which in the closed position of the ring damper sealingly abuts a corresponding sealing means (23; 22) at each axial end of the ports (3), thus preventing the combustion air from flowing through the ports (3) to the burner tip. Each of the sealing means (21, 23; 22, 26) is made of a stainless and heat-resistant material, and each pair of sealing means is constituted by a plane leaf spring (23; 26) the plane of which is substantially perpendicular to the longitudinal axis of the ring damper (20), and a ring (21; 22) with a convex surface on which the leaf spring abuts tangentially in the closed position of the ring damper.