An installation (26) for thermally conditioning thermoplastic preforms (14) that are intended to be formed, the installation (26) including:—a thermal-conditioning zone (40) divided vertically into a heating first part (42) which is intended to house a body (16) of the preform (14) and a cooling second part (44) which is intended to house a neck (20) of the preform (14);—a device (62) for cooling a portion of the preform (14) by producing a stream of gas passing through the thermal-conditioning zone (40); characterized in that the cooling device (62) produces a blade (63) of gas blown with laminar flow through an axial outlet slit (72).