Low profile heat exchanger including a fin plate having opposite facing first and second sides and including a plurality of spaced apart elongate fins that extend outward from the first side and define a plurality of elongate passages that are open facing on the second side, and a flat container having spaced apart cover and shim plates sealably joined about peripheral edges thereof and defining a fluid conducting chamber, the container having an inlet opening and an outlet opening in communication with the fluid conducting chamber to permit a fluid to pass into, through, and out of the fluid conducting chamber, wherein the first side of the fin plate is mounted to the shim plate to permit thermal transfer therebetween and the second side of the fin plate is exposed.