Call yeti and ask them. The outside is probably molded polypropylene or polyethylene (polyethylene is almost impossible to glue to), but I'm not that familiar with them. I would also be very leery of using heat to melt it on, the decal is likely a low melt temp vinyl and if they used a urethane-based foam for insulation, it will turn to mush starting around 160 degrees.
I'd check out some 3M products like VHB tapes and films to see if you can bond it to the decal, and then use the thickness of the tape itself to conform to and bond to the rough cooler surface.