A wall-cooling device for cooling a wall subjected to a heat source and to an outer fluid. The device includes a cooling part with a fastening portion and a cooling portion. The cooling part is made of a thermally-conductive shape-memory alloy having a transition temperature T. The fastener portion is for fastening the device rigidly on a face of the wall. The cooling portion is shaped so that it takes up a first position that is substantially parallel to the wall when the temperature of the wall is lower than the temperature T and so that it takes up a second position in which a plane of the second portion defines, relative to a plane tangential to the wall, a dihedral angle lying in the range 45° to 90° .