An air intake duct of an aircraft engine or other component is provided with a thermal anti-icing system. The front of the air intake duct comprises a toroidal outer skin (16) which forms, with a toroidal internal bulkhead (18), a toroidal plenum (8) about the center line (26). The bulkhead has an inner edge nearest the center line. Within the plenum there is a toroidal inner skin (9) defining with the outer skin a substantially continuous toroidal channel (19). Hot air is supplied via an inlet (7) to the plenum (8). The air flows into an inlet (14) at an end of channel (19) and out of an outlet (11) through the bulkhead (18). This provide more heat to the leading edge of the duct, and to the surface of the duct facing the center line, than to other parts of the duct to prevent build up of ice which may enter, and damage, the engine. This reduces the mass flow of hot air needed for de-icing.