A heat-driven acoustic cooling engine having no moving parts receives heat from a heat source. The acoustic cooling engine comprises an elongated resonant pressure vessel having first and second ends. A compressible fluid having a substantial thermal expansion coefficient and capable of supporting an acoustic standing wave is contained in the resonant pressure vessel. The heat source supplies heat to the first end of the vessel. A first heat exchanger in the vessel is spaced-apart from the first end and receives heat from the first end. A first thermodynamic element is adjacent to the first heat exchanger and converts some of the heat transmitted by the first heat exchanger into acoustic power. A second thermodynamic element has a first end located spaced-apart from the first thermodynamic element and a second end farther away from the first thermodynamic element than is its first end. The first end of the second thermodynamic element heats while its second end cools as a consequence of the acoustic power. A second heat exchanger is adjacent to and between the first and second thermodynamic elements. A heat sink outside of the vessel is thermally coupled to and receives heat from the second heat exchanger. The resonant pressure vessel can include a housing less than one-fourth wavelength in length coupled to a reservoir. The housing can include a reduced diameter portion communicating with the reservoir.