Abstract: An aft aerodynamic fairing for a pylon for attaching an aircraft propelling assembly, including a caisson structure, a heat-shield floor, as well as a support structure for this floor comprising linking parts arranged to link two side edges of this floor to the caisson structure. The linking parts of each side edge of the floor are configured so as to allow travelling motion of the side edge relative to the caisson structure in a corresponding direction included in a plane orthogonal to a longitudinal direction of the fairing. The linking parts form a sliding link between the floor and the caisson structure, reducing the stresses induced by the deformations of these elements in use.