A cooling channel (36, 36B, 63-66) cools inner surfaces (48, 50) of exterior walls (41, 43) of a component (20, 60). Interior side surfaces (52, 54) of the channel converge to a waist (W2), forming an hourglass shaped transverse profile (46). The inner surfaces (48, 50) may have fins (44) aligned with the coolant flow (22). The fins may have a transverse profile (56A, 56B) highest at mid-width of the inner surfaces (48, 50). Turbulators (92) may be provided on the side surfaces (52, 54) of the channel, and may urge the coolant flow toward the inner surfaces (48, 50). Each turbulator (92) may have a peak (97) that defines the waist of the cooling channel. Each turbulator may have a convex upstream side (93). These elements increase coolant flow in the corners (C) of the channel to more uniformly and efficiently cool the exterior walls (41, 43).