From the Mason page linked to above...

NASA claims the spacesuits were cooled by a water system which was piped around the body, then through a system of coils sheltered from the sun in the backpack. NASA claims that water was sprayed on the coils causing a coating of ice to form. The ice then supposedly absorbed the tremendous heat collected in the water and evaporated into space. There are two problems with this that cannot be explained away. 1) The amount of water needed to be carried by the astronauts in order to make this work for even a very small length of time in the direct 55 degrees over the boiling point of water (210 degrees F at sea level on Earth) heat of the sun could not have possibly been carried by the astronauts. 2) NASA has since claimed that they found ice in moon craters. NASA claims that ice sheltered from the direct rays of the sun will NOT evaporate destroying their own bogus "air conditioning" explanation.

Ok. The backpacks did not eject hot water, as stated in an above post, but worked exactly like ant air conditioner or fridge. In any refridgeration unit, gas is compressed into a liquid, thus raising it's temperature. This is the hot bit on the back of your fridge, or the bit with the fans on the roof if an air conditioner. Then this fluid under pressure is released through a small, carefully calibrated nozzle, and because of the pressure drop, turns into a gas. To turn a liquid into a gas requires heat, and this heat is obtained from the pipework the gas is in, and in turn the food in your fridge or the air from your house. This cools the fridge or your house. The gas is then compressed by the pump into a liquid and restarts the cycle. Freon is (was?) used as the working fluid in fridges because the temperature it turns from liquid to gas is quite low, lower than freezing, but not too low as to make it difficult to compress into gas.
The same principle applies to spacecratft and suit cooling, except that it is a 'total loss' system, and a bit back to front. Water is circulated in the suit. This is the hot part of the fridge, usually on the back. There is no need for a compressor as the water can be considered compressed compared to the pressure of the vaccuum outside the suit. A portion of this water passes through a porous plate sublimator, which is analogous to the nozzle in the fridge design. As water seeps out it comes into contact with the vaccuum (if that's the right phrase as you can't touch a vaccuum) and immediately turns to gas because of the pressure drop. This cools the plate to freezing and ice forms, this ice prevents any more water seeping out. So we've got a situation where we have water passing through an ice cold block of metal. More than enough to keep the astronaut cool. What happens when the ice melts due to the warm water passing through the plate? More water seeps out, turns into gas cools the plate and forms more ice. This process can continue until the reservoir of water in the backpack is used up, 8 hours on Apollo 17. To see the same effect of liquids turning into gas when pressure is released, take a spay deodorant can and hold it open for about a minute. Even though there is only a little liquid in these cans, and this liquid has a far lower enthalpy of evaporation than water, the can gets really cold. I've had trouble with gas bottles when camping in the cold freezing and refusing to work because there is not enough background heat to keep the bottle warm. Imagine the same principle, only the gas bottle is full of water on the Moon and is wrapped round an astronaut.

Another part of the argument is that the spacecraft did not carry enough cooling water. This is true. They made the water as they went, as a by-product of the fuel cells which produced electricity. Nothing was wasted. Fred Haise even used the crews urine to top up the cooling water on Apollo 13!