An evaporative cooling apparatus may include a heat transfer module having a vapor passage in fluid communication with a liquid refrigerant in a first container and a heat absorbing module having a drawing liquid selected to absorb the liquid refrigerant in the second container. The heat absorbing module also has a vapor chamber in the drawing fluid that receives vapor generated during evaporation of the liquid refrigerant. The vapor chamber has a selectively permeable membrane that: (i) transports the vapor to the drawing liquid, and (ii) blocks flow of the drawing fluid into the vapor chamber. The refrigerant may be liquid water, the vapor chamber may include a selectively permeable membrane having a pore size between 1 nm and 200 nm, and the drawing fluid may be glycerol.