You are heating the water. A fair proportion of the power you are putting into the system is heating the water so a similar amount of power needed to remove it.
If it is for continuous use then a modified air conditioner (refrigerated) will work.
It really depends on how much heat you need to remove in a given time.
Air is pretty much an insulator of heat, so direct liquid contact with the evaporator surface is needed to do much good.
On the other hand, use the fridge. Leave it on for a week, make a big lot of ice, and put in a drum, or just go down to local ice supply, and buy a few bags.
You would be surprised how 2 or 3 bags in an insulated container filled with water will last. It is fairly easy to calculate how much heat 3 bags of ice can remove.
Or just try it out. 1 bag? 2 bags, 3 bags full sir. You pay for the ice ... the suppliers electricity instead of yours.
Super X3. 3600rpm. Sheridan 6"x24" Lathe + more. Three ways to fix things: The right way, the other way, and maybe your way, which is possibly a faster wrong way.