A blade outer air seal assembly for a gas turbine engine comprising: a seal arc segment (66; 166; 266; 366) including a sealing portion (72; 372) and a pair of opposed rails extending outwardly from the sealing portion (72; 372), the sealing portion (72; 372) including a leading edge portion, a trailing edge portion, and an intermediate portion between the pair of rails, a sealing face dimensioned to bound a core flow path and including a backside face (72C; 172C) opposed to the sealing face, and the backside face (72C; 172C) including a first localized region along the leading edge portion of the seal arc segment (66; 166; 266; 366), a second localized region between the pair of rails, and a third localized region along the trailing edge portion; a support (68; 168; 268; 368) including a mounting portion and a first interface portion (78; 178; 374), the mounting portion attachable to an engine static structure; at least one retention pin (84; 284; 384) dimensioned to engage the first interface portion (78; 178; 374) of the support (68; 168; 268; 368) and at least one of the pair of rails such that the seal arc segment (66; 166; 266; 366) is carried by the at least one retention pin (84; 284; 384); and a support plate (86; 186; 286; 386) arranged relative to the support (68; 168; 268; 368) such that the at least one retention pin (84; 284; 384) is trapped between the support plate (86; 186; 286; 386) and the support (68; 168; 268; 368); wherein a cooling cavity (96; 196; 296; 396) is established between the support (68; 168; 268; 368), the support plate (86; 186; 286; 386), and the second localized region; and wherein the support plate (86; 186; 286; 386) defines at least one cooling passage coupled to the cooling cavity (96; 196; 296; 396), the at least one cooling passage extending along a first passage axis, and a projection of the first passage axis intersecting the first localized region, characterised by conveying a portion of a cooling flow through the at least one cooling passage extending through the support plate (86; 186; 286; 386), wherein the at least one cooling passage is arranged such that the portion of the cooling flow directly impinges on the first localized region of the seal arc segment (66; 166; 266; 366) in operation and a localized temperature of the first localized region approaches a localized temperature of the second localized region. a seal arc segment (66; 166; 266; 366) including a sealing portion (72; 372) and a pair of opposed rails extending outwardly from the sealing portion (72; 372), the sealing portion (72; 372) including a leading edge portion, a trailing edge portion, and an intermediate portion between the pair of rails, a sealing face dimensioned to bound a core flow path and including a backside face (72C; 172C) opposed to the sealing face, and the backside face (72C; 172C) including a first localized region along the leading edge portion of the seal arc segment (66; 166; 266; 366), a second localized region between the pair of rails, and a third localized region along the trailing edge portion; a support (68; 168; 268; 368) including a mounting portion and a first interface portion (78; 178; 374), the mounting portion attachable to an engine static structure; at least one retention pin (84; 284; 384) dimensioned to engage the first interface portion (78; 178; 374) of the support (68; 168; 268; 368) and at least one of the pair of rails such that the seal arc segment (66; 166; 266; 366) is carried by the at least one retention pin (84; 284; 384); and a support plate (86; 186; 286; 386) arranged relative to the support (68; 168; 268; 368) such that the at least one retention pin (84; 284; 384) is trapped between the support plate (86; 186; 286; 386) and the support (68; 168; 268; 368); wherein a cooling cavity (96; 196; 296; 396) is established between the support (68; 168; 268; 368), the support plate (86; 186; 286; 386), and the second localized region; and wherein the support plate (86; 186; 286; 386) defines at least one cooling passage coupled to the cooling cavity (96; 196; 296; 396), the at least one cooling passage extending along a first passage axis, and a projection of the first passage axis intersecting the first localized region, characterised by conveying a portion of a cooling flow through the at least one cooling passage extending through the support plate (86; 186; 286; 386), wherein the at least one cooling passage is arranged such that the portion of the cooling flow directly impinges on the first localized region of the seal arc segment (66; 166; 266; 366) in operation and a localized temperature of the first localized region approaches a localized temperature of the second localized region.