A gas turbine engine comprising: a high-pressure turbine; a low-pressure turbine downstream of the high-pressure turbine and having a LPT outer case and a LPT plenum extending circumferentially around a central axis, the LPT plenum distributing cooling air around the low-pressure turbine; a mid-turbine frame assembly connecting the low-pressure turbine and the high-pressure turbine, the mid-turbine frame assembly having: a mid-turbine frame outer case defining an inlet for connection to a source of the cooling air, an intermediary plenum fluidly connected to the source of cooling air via the inlet, the intermediary plenum having a first air outlet and a second air outlet, and a mid-turbine frame plenum disposed radially inwardly of the mid-turbine frame outer case and fluidly connected to the source of the cooling air via the first air outlet of the intermediary plenum; a cooling air conduit fluidly connecting the second air outlet of the intermediary plenum to the LPT plenum while bypassing the mid-turbine frame plenum; and two protrusions (95A, 95B) being axially spaced apart from one another relative to the central axis and extending from the mid-turbine frame outer case in a direction having a radial component relative to the central axis, the two protrusions (95A, 95B) extending circumferentially around the central axis, the intermediary plenum being disposed between the two protrusions (95A, 95B), characterised in that the first air outlet is a first aperture defined through a first protrusion of the two protrusions, and the second air outlet is a second aperture defined through a second protrusion of the two protrusions. a high-pressure turbine; a low-pressure turbine downstream of the high-pressure turbine and having a LPT outer case and a LPT plenum extending circumferentially around a central axis, the LPT plenum distributing cooling air around the low-pressure turbine; a mid-turbine frame assembly connecting the low-pressure turbine and the high-pressure turbine, the mid-turbine frame assembly having: a mid-turbine frame outer case defining an inlet for connection to a source of the cooling air, an intermediary plenum fluidly connected to the source of cooling air via the inlet, the intermediary plenum having a first air outlet and a second air outlet, and a mid-turbine frame plenum disposed radially inwardly of the mid-turbine frame outer case and fluidly connected to the source of the cooling air via the first air outlet of the intermediary plenum; a mid-turbine frame outer case defining an inlet for connection to a source of the cooling air, an intermediary plenum fluidly connected to the source of cooling air via the inlet, the intermediary plenum having a first air outlet and a second air outlet, and a mid-turbine frame plenum disposed radially inwardly of the mid-turbine frame outer case and fluidly connected to the source of the cooling air via the first air outlet of the intermediary plenum; a cooling air conduit fluidly connecting the second air outlet of the intermediary plenum to the LPT plenum while bypassing the mid-turbine frame plenum; and two protrusions (95A, 95B) being axially spaced apart from one another relative to the central axis and extending from the mid-turbine frame outer case in a direction having a radial component relative to the central axis, the two protrusions (95A, 95B) extending circumferentially around the central axis, the intermediary plenum being disposed between the two protrusions (95A, 95B), characterised in that the first air outlet is a first aperture defined through a first protrusion of the two protrusions, and the second air outlet is a second aperture defined through a second protrusion of the two protrusions.