Previously I had thought the only productive way to use heat directly to cause cooling was an adsorption/absorption cooler. There, heat is used to drive a working fluid (water, methanol, ammonia) from an adsorbant (activated charcoal, alumina, aerogel) or absorbant (salt water) which is condensed at ambient temperature. Then, the sorbant is cooled to ambient temperature, and it becomes hungry for the working fluid, pulling the vapors in and casing a vacuum. Thus the working fluid is boiling in a vacuum and drops below ambient temp.
The most common implementation of this is ammonia and salt water. This is used in industry and was used to make ice in the days before abundant electricity (see Icy Ball).
Another type of refrigerator
There is another way of pulling a vacuum, and thus another way to boil a working fluid below atmospheric pressure; another way to refrigerate. This uses an aspirator, or a steam ejector. Moderate pressure steam is forced out a nozzle and entrains (smashes into and accelerates) gas outside the nozzle. In this way, the gas smashed into is removed and new gas rushes in to replace it, and then is also smashed into. Thus a vacuum results.
This paper is a students analysis of a water/water system (steam used to evaporate water). He achieves an efficiency (COP) of 50% using steam at 120C (very low temp for achieving useful work). I believe this is well above what adsorption systems achieve. Carnot efficiency of a system evaporating at 120C and condensing at 100C would be practically nil, so this blows a steam engine refrigeration system out of the water. I expect using methanol as a working fluid would be even more efficient as long as the waste heat could be used to distill the methanol. Methanol distills much more easily than ethanol because it does not form an azeotropic mixture.