A bit of an odd request, but we've gotten it now like 5 times so we wanted to post an FAQ. The long and short of it is NO, we don't recommend soaking / sticking your Bucket inside another water filled container for extended periods of time.
If you really want to do good temperature control, just buy our FTSs temp control system for the Brew Bucket now available on our site!!!
Below we have pasted in a reply from one of our Support Team to a customer for your reference:
That's a question we haven't had before. While in theory, yes you could. In practice not really recommended either.
If you do this, you might expect some discoloration on the outside of your Bucket. And you should keep in mind that you are basically creating an incubator for bacteria. for (though it's on the outside of your bucket, you need to be really sure you sanitize the racking port!)
If your water is "ideal" then you won't have any issues. But if you have high mineral concentrations in your water, you are likely to have some issues.
If the water is high in oxygen, you might develop some surface rust, as even the highest grades of Stainless steel will exhibit surface rust under certain conditions. The stains should be cleanable with product like Bar Keeper's Friend and or Lime-away (be sure to see our warnings about Bar Keeper’s Friend relative to etched gallon markings and logo etch!)