A hot section part of a turbine engine configured to be exposed to hot gases, the hot section part comprising: a first wall having a first wall inner surface and a first wall outer surface opposite the first wall inner surface, the first wall inner surface exposed to the hot gases; a second wall extending around at least a portion of the first wall to form a dual-wall structure, the second wall having a second wall inner surface and a second wall outer surface opposite the second wall inner surface, the second wall inner surface spaced apart from the first wall outer surface to form an intervening cavity; a plurality of pedestals, each pedestal coupled to the first wall outer surface and the second wall inner surface and extending through the intervening cavity, each pedestal having at least one outside surface facing the intervening cavity, and each pedestal having a principal axis and extending through the intervening cavity about its principal axis; a plurality of impingement cooling holes extending through the second wall to admit a flow of cooling air into the intervening cavity; a plurality of effusion cooling passages, each effusion cooling passage associated with a different one of the plurality of pedestals and disposed at a predetermined angle relative to its associated principal axis, each effusion cooling passage having an inlet and an outlet, each inlet formed on a different one of the at least one outside surface of the plurality of pedestals, each outlet formed on the first wall outer surface, whereby 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; characterized in that a plurality of heat transfer enhancement features are formed on at least portions of the second wall outer surface and on surfaces that define the intervening cavity; or in that at least a portion of the second wall around the impingement cooling holes are locally dimpled in a direction away from the intervening cavity. a first wall having a first wall inner surface and a first wall outer surface opposite the first wall inner surface, the first wall inner surface exposed to the hot gases; a second wall extending around at least a portion of the first wall to form a dual-wall structure, the second wall having a second wall inner surface and a second wall outer surface opposite the second wall inner surface, the second wall inner surface spaced apart from the first wall outer surface to form an intervening cavity; a plurality of pedestals, each pedestal coupled to the first wall outer surface and the second wall inner surface and extending through the intervening cavity, each pedestal having at least one outside surface facing the intervening cavity, and each pedestal having a principal axis and extending through the intervening cavity about its principal axis; a plurality of impingement cooling holes extending through the second wall to admit a flow of cooling air into the intervening cavity; a plurality of effusion cooling passages, each effusion cooling passage associated with a different one of the plurality of pedestals and disposed at a predetermined angle relative to its associated principal axis, each effusion cooling passage having an inlet and an outlet, each inlet formed on a different one of the at least one outside surface of the plurality of pedestals, each outlet formed on the first wall outer surface, whereby 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; characterized in that a plurality of heat transfer enhancement features are formed on at least portions of the second wall outer surface and on surfaces that define the intervening cavity; or in that at least a portion of the second wall around the impingement cooling holes are locally dimpled in a direction away from the intervening cavity.