That's the problem, removing heat at a sufficient rate. Of course it can be done, but the most efficient way (in terms of cost) is just open loop evaporation.

I'm not a datacenter engineer, but I used to work in the ski industry. Snowmaking systems use vast quantities of compressed air. It works better if that air is cool. Blowing hot compressed air out of a snow cannon means the air temperature (wet bulb to be specific) needs to be colder to make snow.

Anyways, most air compression stations use water to cool the air, and then evaporative coolers to cool the water. The water is reused, but a ton (not sure of the percentage) is lost into the air. It's more or less a tower with a big fan on top, and water percolates down from the top, being cooled by the air as it goes. The water is then collected and pumped through the system again (but of course has to be always topped up to counteract what was lost to evaporation).

Anyways, long story short is it's most cost effective to just spray water into the air to cool water, as long as water is free/cheap.