A process for manufacturing a tire includes providing an elastomeric layer on an outer surface of a toroidal support, manufacturing the tire on the toroidal support provided with the elastomeric layer, introducing the tire supported on the toroidal support into a moulding cavity, introducing a fluid under pressure into a space defined between the toroidal support and an inner surface of the tire in order to press an outer surface of the tire against walls of the moulding cavity, and curing the tire. The elastomeric layer forms an inner circumferential surface of the tire. The process further includes causing an electrical current to flow in at least one heating element provided to the outer surface of the toroidal support so as to obtain at least partial precuring of the elastomeric layer. A toroidal support for carrying out the process is also disclosed.