Turbomachine module provided with a device to improve radial clearances

The invention relates to a turbomachine module comprising a device to improve radial clearances, comprising an outer casing, an inner casing and at least one shock absorbing ring connecting the casings, the module also comprising an annular cavity on the downstream side of the ring, with a passage formed in it through which an airflow is drawn off from the primary flow (Fp). According to the invention, the device to improve radial clearances comprises a thermal inertia control device for the shock absorbing ring mounted on the shock absorbing ring, downstream from it, this device comprising at least one coat of thermal insulation, and at least partly delimiting the annular cavity on the downstream side of it.