A microchannel crossflow fluid heat exchanger and a method for its fabrication are disclosed. The heat exchanger is formed from a stack of thin metal sheets which are bonded together. The stack consists of alternating slotted and unslotted sheets. Each of the slotted sheets includes multiple parallel slots which form fluid flow channels when sandwiched between the unslotted sheets. Successive slotted sheets in the stack are rotated ninety degrees with respect to one another so as to form two sets of orthogonally extending fluid flow channels which are arranged in a crossflow configuration. The heat exchanger has a high surface to volume ratio, a small dead volume, a high heat transfer coefficient, and is suitable for use with fluids under high pressures. The heat exchanger has particular application in a Stirling engine that utilizes a liquid as the working substance.