A ironing machine (1) comprising: an axially-rotatable ironing drum (4); a motor assembly adapted to drive the ironing drum (4) into rotation about the drum longitudinal axis (A); an ironing chest (7) which is arranged adjacent to the ironing drum (4), locally substantially parallel to the peripheral surface (4p) of said ironing drum (4); a supporting assembly (9) adapted to keep the ironing drum (4) and the ironing chest (7) adjacent to one another; and an induction device (10) which is located adjacent to the ironing chest (7) and is adapted to heat up, via electromagnetic induction, the ironing chest (7); said ironing chest (7) comprising a platelike member (13) which extends beside the ironing drum (4), is substantially C-bent so as to extend locally substantially parallel to the peripheral surface (4p) of said ironing drum (4), and has a multilayer structure that includes: a main supporting sheet (14) which is substantially C-bent and is made of a metal material having a given thermal conductivity; and a ferromagnetic layer (15) which covers the convex face of said main supporting sheet (14), and is made of a ferromagnetic metal material having a thermal conductivity lower than that of the metal material forming said main supporting sheet (14).