A turbine shroud assembly (22, 222) comprising: a carrier (24, 224) configured to be coupled to a turbine case so as to fix other components of the turbine shroud assembly (22, 222) relative to the turbine case, a blade track segment (26, 226) comprising ceramic matrix composite materials, the blade track segment (26, 226) including a runner (30, 230) that extends at least partway about a central axis having a flow surface (32, 232) arranged to define a gas flow path and an exterior surface (33, 233) spaced radially outward of the flow surface (32, 232) relative to the central axis and an attachment member (31, 231) that extends radially outward from the exterior surface (33, 233) of the runner (30, 230), and a mounting assembly (28, 228) comprising a first metallic material configured to couple the blade track segment (26, 226) to the carrier (24, 224), the mounting assembly (28, 228) including a forward hanger (42, 242) that extends radially inward from the carrier (24, 224) and engages the attachment member (31, 231) of the blade track segment (26, 226) to block radially inward movement of the blade track segment (26, 226) relative to the carrier (24, 224), an aft hanger (43, 243) spaced axially aft of the forward hanger (42, 242) that extends radially inward from the carrier (24, 224) and engages the attachment member (31, 231) of the blade track segment (26, 226) to block radially inward movement of the blade track segment (26, 226) relative to the carrier (24, 224), the forward and aft hangers (42, 242, 43, 243) each having a radially-inwardly facing surface (46, 246) arranged in confronting relation to the exterior surface (33, 233) of the runner (30, 230) such that heat conducted from the flow surface (32, 232) of the runner (30, 230) to the exterior surface (33, 233) of the runner (30, 230) radiates toward the radially-inwardly facing surface (46, 246) of the forward and aft hangers (42, 242, 43, 243), and hanger heat shields (44, 244, 45, 245), each comprising a second metallic material different from the first metallic material, and characterised in that each hanger heat shield (44, 244, 45, 245) is arranged radially between the exterior surface (33, 233) of the runner (30, 230) and the radially-inwardly facing surfaces (46, 246) of the forward and aft hangers (42, 242, 43, 243) to reduce the amount of heat transfer to the forward and aft hangers (42, 242, 43, 243) from the exterior surface (33, 233) of the runner (30, 230) during use of the turbine shroud assembly (22, 222). a carrier (24, 224) configured to be coupled to a turbine case so as to fix other components of the turbine shroud assembly (22, 222) relative to the turbine case, a blade track segment (26, 226) comprising ceramic matrix composite materials, the blade track segment (26, 226) including a runner (30, 230) that extends at least partway about a central axis having a flow surface (32, 232) arranged to define a gas flow path and an exterior surface (33, 233) spaced radially outward of the flow surface (32, 232) relative to the central axis and an attachment member (31, 231) that extends radially outward from the exterior surface (33, 233) of the runner (30, 230), and a mounting assembly (28, 228) comprising a first metallic material configured to couple the blade track segment (26, 226) to the carrier (24, 224), the mounting assembly (28, 228) including a forward hanger (42, 242) that extends radially inward from the carrier (24, 224) and engages the attachment member (31, 231) of the blade track segment (26, 226) to block radially inward movement of the blade track segment (26, 226) relative to the carrier (24, 224), an aft hanger (43, 243) spaced axially aft of the forward hanger (42, 242) that extends radially inward from the carrier (24, 224) and engages the attachment member (31, 231) of the blade track segment (26, 226) to block radially inward movement of the blade track segment (26, 226) relative to the carrier (24, 224), the forward and aft hangers (42, 242, 43, 243) each having a radially-inwardly facing surface (46, 246) arranged in confronting relation to the exterior surface (33, 233) of the runner (30, 230) such that heat conducted from the flow surface (32, 232) of the runner (30, 230) to the exterior surface (33, 233) of the runner (30, 230) radiates toward the radially-inwardly facing surface (46, 246) of the forward and aft hangers (42, 242, 43, 243), and hanger heat shields (44, 244, 45, 245), each comprising a second metallic material different from the first metallic material, and characterised in that each hanger heat shield (44, 244, 45, 245) is arranged radially between the exterior surface (33, 233) of the runner (30, 230) and the radially-inwardly facing surfaces (46, 246) of the forward and aft hangers (42, 242, 43, 243) to reduce the amount of heat transfer to the forward and aft hangers (42, 242, 43, 243) from the exterior surface (33, 233) of the runner (30, 230) during use of the turbine shroud assembly (22, 222).