Gas turbine transition piece with dimpled surface and cooling method for such a transition piece

A transition piece assembly (42) for a gas turbine includes a transition piece (44) having one end adapted for connection to a gas turbine combustor and an opposite end adapted for connection to a first turbine stage; the transition piece has an exterior surface formed with a plurality of concave dimples (48) thereon. An impingement flow sleeve (46) surrounds the transition piece, establishing a plenum (54) therebetween. The impingement sleeve is formed with a plurality of cooling apertures (52) therein for introducing compressor cooling air into the plenum.