Been using a 5 gal bucket with styrofoam bucket line. Put hole in upper side of bucket for hose. Can run battery bubbler or my onboard bubbler. Have never had a problem keeping minnows up to a pound or so at all and it gets bad hot here in summer. Friend built a minnow cooler like your talking about. Works like a charm. All your trying to do is keep water at a temp they can tolerate. In summer I freeze the small gator aid bottles full of water, put several in my drink cooler swap out ever hour or so and that keeps water plenty cool with that bucket liner. Only advantage on the cooler type I can see is very unlikely you will turn it over. One main thing I have found on conversions is having a insulated lid to keep sun from heating up inside.
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Charlie Weaver USN/ENC 1965-1979