A gas turbine engine comprising: a compressor for compressing air to generate compressed air; a combustor for combusting fuel with the compressed air to generate combustion gas; a turbine supported for rotation about an axis so that it is driven to rotate by the contact with the combustion gas; an exhaust diffuser having inner and outer cones (47,45) both arranged coaxially with the axis to define an annular exhaust channel therebetween and a central cavity within the inner cone; a first path extending radially through the outer and inner cones (45,47), the first path having a radially inward end and a radially outward end, the inward end being fluidly connected to the central cavity; an air supply fluidly connected to the radially outward end of the first path and for drawing cooling air, by using a part of the compressed air, through the first path into the central cavity; a housing surrounding the outer cone to define a peripheral cavity between the housing and the outer cone; and a second path extending radially through the outer and the inner cones (45,47) and the exhaust channel and fluidly connecting between the central and the peripheral cavities (S1, S2); characterised by a first opening defined in the inner cone to fluidly connect between the exhaust channel and the central cavity, the first path and the first opening being so positioned that the cooling air is delivered from the air supply through the first path, the central cavity, and the first opening into the exhaust channel as it makes thermal contact with an object positioned in the central cavity to cool the object; and a second opening fluidly connecting between the peripheral cavity and the exhaust channel; said second path being positioned so that, after making the thermal contact with the object, a part of the cooling air in the central cavity is delivered through the second path, the peripheral cavity and the second opening into the exhaust channel. a compressor for compressing air to generate compressed air; a combustor for combusting fuel with the compressed air to generate combustion gas; a turbine supported for rotation about an axis so that it is driven to rotate by the contact with the combustion gas; an exhaust diffuser having inner and outer cones (47,45) both arranged coaxially with the axis to define an annular exhaust channel therebetween and a central cavity within the inner cone; a first path extending radially through the outer and inner cones (45,47), the first path having a radially inward end and a radially outward end, the inward end being fluidly connected to the central cavity; an air supply fluidly connected to the radially outward end of the first path and for drawing cooling air, by using a part of the compressed air, through the first path into the central cavity; a housing surrounding the outer cone to define a peripheral cavity between the housing and the outer cone; and a second path extending radially through the outer and the inner cones (45,47) and the exhaust channel and fluidly connecting between the central and the peripheral cavities (S1, S2); characterised by a first opening defined in the inner cone to fluidly connect between the exhaust channel and the central cavity, the first path and the first opening being so positioned that the cooling air is delivered from the air supply through the first path, the central cavity, and the first opening into the exhaust channel as it makes thermal contact with an object positioned in the central cavity to cool the object; and a second opening fluidly connecting between the peripheral cavity and the exhaust channel; said second path being positioned so that, after making the thermal contact with the object, a part of the cooling air in the central cavity is delivered through the second path, the peripheral cavity and the second opening into the exhaust channel.