[aruametello]

in short: the tub idea would work but feels a bit cubersome.

a different approach to possibility the same target results would be to use "Termoeletric cooling" (https://en.wikipedia.org/wiki/Thermoelectric_cooling) often described as TEC/peltier to cold down a surface (metal surface in your loop?) to bellow air temperature.

the short description: it is a device has a hot side that will be kept X degrees above the cold side, so if the X of your tec is "50 ish", if you cool the hot side to 60c, the cold side will be 10c. (its often easy to go bellow 0c)

now the bad news... they are VERY power inefficient, you might spend 200w 12v DC on it to pull of 100w of heat on the cold side, so not for the "power consumption conscious" crowd. those are handy to create a cold water drinking fountain because they can be toggled quickly. (perhalps just run it when needed?)