The system makes it possible to reduce the clearances existing between the rotor and stator of a turbine (40) of a turbo jet engine during the various operating phases of the latter whilst keeping the temperatures of the disks inside the limits of their mechanical behaviour. The disks (4) of the turbine (40) are ventilated via the sampling of high pressure air at a high temperature (2) and the stator via the sampling of low pressure air at a low temperature (3). The respective temperatures of these two samplings are homogenized by a heat exchanger (1). This exchanger is short-circuited by a branch circuit connection (5) on the low pressure circuit so as to keep as stable as possible the clearances inside the turbine (40) according to the various ranges of capacity of the turbo jet engine by means of a valve (6) controlled by the computer.Application for aircraft turbo jet engines.