Hi Jay, I don't have any experience with riding with a carrier on the back of a bike, but I have seen it here. I live in Canada and our climate is cooler than you would have in Texas. He would be fine being pulled in the carrier as he wouldn't be exerting himself in there, or running beside you, but my only concern would be if the temperatures were hot outside, and he was inside the plastic carrier with the door zipped up. It may get too hot inside for him, especially if he was in there for 45 mins or longer as you plan to do. I'm not sure if these carriers get hot inside or not, maybe another member knows more about this, or has experience with it. I hope it works out for you, it sounds like fun. Please share what you find out.