An aircraft nacelle including a pipe (32), a peripheral wall (34), a lip (36), and a front frame (38) connecting the peripheral wall (34) and the pipe (32) and forming with the lip (36) a space (50) in which the hot air that is provided for frost treatment can circulate, with the pipe (32) including a coating (44) for the composite material acoustic treatment, is characterized in that the nacelle includes at least one element (52) made of a heat-conducting material inserted between the lip (36) and the pipe (32) ensuring the continuity of the aerodynamic surfaces of the lip (36) and the pipe (32) and the propagation of heat from the space (50) toward the rear of the nacelle, whereby the at least one element (52) includes a coating (54) for acoustic treatment that is made of a heat-resistant material.