A cooling channel (36, 36B) cools an exterior surface (40 or 42) or two opposed exterior surfaces (40 and 42). The channel has a near-wall inner surface (48, 50) with a width (W1). Interior side surfaces (52, 54) may converge to a reduced channel width (W2). The near-wall inner surface (48, 50) may have fins (44) aligned with a coolant flow (22). The fins may highest at mid-width of the near-wall inner surface. A two-sided cooling channel (36) may have two near-wall inner surfaces (48, 50) parallel to two respective exterior surfaces (40, 42), and may have an hourglass shaped transverse sectional profile. The tapered channel width (W1, W2) and the fin height profile (56A, 56B) increases cooling flow (22) into the corners (C) of the channel for more uniform and efficient cooling.