A hot section part of a turbine engine configured to be exposed to hot gases includes a first wall, a second wall, a plurality of pedestals, a plurality of impingement cooling holes, and a plurality of effusion cooling passages. The walls are spaced apart to form an intervening cavity, and each pedestal extends through the intervening cavity. The impingement cooling holes extend through the second wall to admit a flow of cooling air into the intervening cavity. Each effusion cooling passage is associated with a different one of the plurality of pedestals and is disposed at a predetermined angle relative to its associated principal axis. A portion of the flow of cooling air admitted to the intervening cavity is directed through at least a portion of each of the plurality of pedestals and onto the first wall inner surface.