What to put underneath a polycarbonate sous vide bath container?
A trivet is what you want.  Any store with cookery goods will probably have some.  They run from about five to well over thirty dollars depending on quality, effectiveness, fanciness, and decorative appeal.

I prefer the solid ones with feet for really hot pots or continuous heating.  

I often successfully use one or more folded tea or bath towels or even a wooden plank (6" x 6", e.g.).