The point about the cabinet was to illustrate how cooling of this equipment is inexpensive , easily and simply done without the need for A/C equipment ...... air flow and fans is all that's needed for most applications.
Depending upon the number of units, a computer cooling system using a liquid coolant might be a sensible solution. Certainty is quieter. Probably cost about $250 a machine.
I opted to replace the stock CPU cooler/fan assemblies with Ninja CPU coolers for our studio computers, which always lived in their own closets anyway. Cost about $60.
Don't forget about the clear cases with funky neon lights. :D
Are you chilling the amps , sound processors and mixers in the studio?
In my view a portable ac unit can do well in this case, you can choose between a number of options between the companies manufacturing the unit.I'm suggesting this to you because it is sufficient for a room to maintain an appropriate temperature.
The normal temperature in most offices will be kept inside the proper zone for the equipment, so your problem is just in getting enough air movement through the space to maintain. Any source of incoming air should be filtered to lessen problems with lint and daily dirt, air coming through a louver or under the door isn't clean. If possible, consider drawing air from an adjoining space through a filter, outflow could be done through a louver vent above the closet door.
Whether in the office or at home, are very necessary own a cooling for a computer room