Welcome to HBT -
That might work, haven't heard of it here, yet. Try if you want, let us know!
other common options are to find a cheap tub from wally-world and set your pail into that, fill with water, and float some frozen water bottles in it. Keep some in the freezer, and swap them out as needed. In the cooler climates, you can drop an aquarium heater in it.
Or, same thing, but drape a t-shirt over it, so it soaks up the water and holds it against the sides - then blow a fan on it to get some evaporative cooling.
A large ice chest / cooler (70qt IceCube?) might hold that pail and hold temps better than a wally-world tub...
Search under fermentation control, and Swamp cooler for ideas -
