We had a largish cooler for fishing. I ended up putting a towel in the bottom of the cooler to absorb vibrations, closed the lid over the power cord. I checked the temperature a bunch at first to check for overheating, but it wasn't an issue.

We didn't keep at it long, but that kept the noise from being an issue. It was a slow, messy process and we were too busy to pay attention to it over long periods of time.