A method for producing a curved profile from a rectilinear preform of preimpregnated fiber webs, including stacking webs on the deformable mandrel and winding the deformable mandrel and the stacked webs on a bending tool along an axis of rotation (X), the profile including a stack of N webs, at least one first part of the profile being positioned in a plane perpendicular to the axis of rotation (X) and at least one second part parallel to the axis (X) whereof a face can be in contact with the bending tool. The method includes stacking the N fiber webs on the deformable mandrel, generating a heat gradient between the face and the rest of the preform that is hotter than the face, bending, in a single phase, the N webs inserted between the deformable mandrel and the bending tool, and polymerizing the N bent webs.