Annular or ring-segment-shaped cavities (2, 7) which are formed in particular in multi-shell (11; 12, 13) casings of turbomachines are preferably provided with suitable means for compensating for forming temperature stratifications. According to the invention, an overflow passage (14) connects two points of the cavity to one another which are situated in different circumferential positions. Arranged in the overflow passage (14) is an ejector (17) which can be operated with a motive fluid and which serves to drive a flow through the overflow passage from an upstream end (15) to a downstream end (16).