A sheet metal sealing sleeve placed under a pair of juxtaposed blade platforms in a turbomachine so as to cover the gap between them is provided with apertures to allow the flow of a ventilating gas to the platforms. The apertures are provided in bosses formed on the sleeve to define chambers between the sleeve and the platforms which provide for greater heat exchange by virtue of the forcible impact of the gas blown through the apertures under the platforms. The sleeve also aids in damping platform vibration.