I use a barrel wrap I made, I keep it wet with a spray bottle for mirage and heat. I shoot many thousands of Pdogs yearly and have yet to see a better way for what/how I shoot them. Ive run 30-40 round strings and have not had the barrel HOT, warm sure, but that wetness draws heat fast and no issues with mirage due to barrel heat ever.
OK here it is. Just a cotton t-shirt, doubled up, sewed, then folded over and gave a bottom sew, double your sewing so it dont tear, split it at your forend, sew edges and its done. Worried about looks...who cares it just works!
Its split right at the forearm and then slids under the scope, Velcro strip to strap it around the chamber, wet down and go shooting. Make sure you have a spray bottle and wet it when you start to see it dry out. I use up a gallon of water per day of p-doggong if its hot & sunny.