Briefly described, the present invention is concerned with cooling heated bodies and/or heated fluid with synthetic jet actuators in either open or closed systems. A first preferred embodiment of a cooling system of the present invention comprises a synthetic jet actuator directed to impinge directly on a heat producing (or heated) body. The synthetic jet actuator generates a synthetic jet stream comprised of cool ambient fluid that impinges on the heated surface thereby cooling this surface. As an example, the heated surface/body could be a microchip array in a microcomputer. After coming into contact with the heated surface, the fluid moves along the surface and is finally rejected to the ambient where it mixes and cools down. The synthetic jet may be incorporated into a modular unit that may be clipped on to a circuit board or other heat producing element to provide added, `ad hoc` cooling. In another configuration, a synthetic jet actuator may be positioned, relative to the heated surface, to create a synthetic jet stream to flow along the heated surface. In this embodiment, the flow would be approximately tangential to a surface of a heat producing body. This embodiment may further comprise a cyclical flow of the fluid jet, along the heated body and about a heat sink surface.