A surface cooled heat exchanger including a stack of elongate plate pairs, each plate pair including first and second plates having elongate central portions surrounded by sealably joined edge portions with a fluid passage defined between the central portions; each plate pair having spaced apart inlet and outlet openings that are connected together for the flow of fluid through the fluid passages; each plate pair having an exposed fin plate extending peripherally outward from the joined edge portions along a length of the plate pair. Each fin plate may have a varying edge profile along an outwardly extending edge thereof.