Obviously, in a vacuum two of the three standard mechanisms of heat transfer are ineffective: conduction and convection require a medium. But radiation is still effective, and this is used by satellites to maintain thermal balance (either passively, through the so-called "slow-roast" mode as was used in the Apollo capsules enroute to the moon, or actively, with thermal transfer elements inside the satellite to pipe heat from "hot" sides to cool radiative elements.) However, one other mechanism is available for cooling is evaporation. Yes, evaporation! This was used as the principal thermal management tool in the Lunar Excursion Vehicle (LEM) used for landing on the moon: hot fluid from the cooling system evaporated water away into the vacuum of space to keep the cooling system of the LEM within temperature limits.
During the use of the LEM of Apollo 13 as a "lifeboat" in returning that crew safely, a major concern was that enough cooling water would exist to allow the LEM systems to operate through the return voyage. I am not well-versed in the specific arrangements made in the Apollo lunar excursion suits, but I suspect that evaporative cooling was used to carry away waste heat from these units, much like in the LEM. It's a simple, lightweight system, requiring no large radiating element to be kept out of sunlight, and for the short period of time the suits were used, would require a relatively small amount of water. Think of it as duplicating the body's own sweat-cooling system in the infrastructure of the suit.
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