A process for manufacturing a tire by the steps of producing and assembling the tire structural elements on a toroidal support to form a green tire, and the step of precuring at least an inner surface of the green tire by heating the toroidal support. The radially inner surface of the toroidal support is provided with a plurality of protruding elements to reduce the time required for the outer surface of the toroidal support to reach a temperature which is suitable for ensuring a uniform and homogeneous precuring of the inner surface of the green tire, preferably of the inner surface and the bead regions of the green tire.