A fiber application machine for the production of parts made of composite materials comprising a compacting roller for applying on an application surface a band formed of at least a resin pre-impregnated flat fiber, and a heating system able to emit a heat radiation towards the band. The compacting roller comprises a rigid central tube provided with radial holes, and a cylinder made of an elastically deformable, flexible material, assembled on the central tube, and having a fluid communication assembly that brings the radial holes into fluid communication with the external surface of the cylinder. The machine includes a thermal regulation system that injects a thermal regulation fluid in the central tube internal passage.