Hi i hope this helps,i bought the coolers and wine bottle holders precut so that made it easy to hoop. I hooped two layers of tearaway,pined the coolers in the hoop [make sure pins are well out of the way of the stich line] and embroidered as normal. Then removed the cooler turned them right side together and zigzaged them together making sure that a locking or reverse stich was used on the outside edges to stop them pulling apart. If the cooler has been premade i would split the side seams open so you can hoop them. I used black tearaway it looks much better. These make great gifts.

Donna, does the liner separate? If so, I would separate it and stitch on the outer portion. If you go through all you puncture the thermal/cooler. If it can't be separated, I'd take and stitch your design out on a felt with iron on backing and press it on or use fabri-tac and glue it on. It will stay with fabri tac