A process for manufacturing a plastic hollow body by molding two sheets of molten plastic in a mold including two cavities, the process including: a) two molten plastic sheets are manufactured by extrusion of at least one stream of molten plastic and transverse cutting thereof; b) these sheets are introduced between the mold cavities; c) the mold is closed and the hollow body is manufactured by conforming the two sheets to the mold cavities; d) the hollow body thus obtained is removed from the mold; e) all of operations a) to d) are repeated to manufacture another hollow body from two new sheets; and before, during, or after the transverse cutting operation, the lower portion of the two new sheets is cooled using a specific device that makes possible a local cooling of the sheets in the lower portion.