I've learned something from my Fresno CA Health Department last week. You can propose to them saying that you will only cook hotdogs that you can fit into your steam pan before heading out of your commissary. It'll allow you to pass the mechanical refrigeration part. Not 100% sure your HD will let you, but we're both in CA. Worth a shot.
(Although of course you can just bring hot dogs with you and do it at the site, and bring extras and just leave a small hidden ice chest with extra dogs in the car, illegal though if you want to risk. I think one or two steam pan full of dogs is more than enough though.)