A fuselage (2, 2', 2") for a convertible aircraft (1) is described, comprising a nose (4) and a tail (5) arranged on mutually opposite sides along a first longitudinal axis (Y) of the fuselage (2); a first portion (100) and a second portion (101) arranged one after the other, proceeding along the first axis (Y) from the nose (4) towards the tail (5); and an electric power source (102) connectable with at least one electric powertrain (40a, 40b, 40c, 40d, 40e, 40f) and arranged inside the second portion (101); the first and second portion (100, 101) define respectively a first and a second section (110, 111, 111") in a plane orthogonal to the first axis (Y); the second section (111) defines at least one air intake (120) that is open towards the outside of the fuselage (2) itself and fluidically connected with the source (102) so as to convey, in use, a flow of cooling air onto the source (102) itself following the forward motion of the aircraft (1); the second section (111, 111") having a larger area than the first section (110); the air intake (120) being arranged at a sidewall (19) of the second portion (101) and externally to the first portion (100) and in a view parallel to the first axis (Y).