As we Phoenicians brave today's high temps–threatening 119°–I am inspired to plead the masses not to walk a dog in the middle of the day. I mean, please. I can't believe how many dogs I saw out for a walk when driving home from my mid-day visits today. Really? Would you want to walk on the scorching asphalt with your bare feet? Try it.
Dogs' paws can burn, and burn bad. They are a bit more tolerant of the immediate sensation when walking on a hot surface because their paws are pretty tough, but damage is done. The dog may limp, lick their paws, or show other signs of distress several hours after the burn occurs.
My rule of thumb is to never walk a dog when the temperature is over 100°. I let my clients know that I'll be happy to do some rigorous indoor play, or a nice game of fetch in the grass if it's not too hot out.
Instead of walking your dog at noon, consider a early-morning or late-evening stroll. Be aware that concrete and asphalt can hold heat well past sundown, so test it with your own bare foot before proceeding. If you can comfortably stand, you're good to go.
You can also try dog booties for protection.
So if you don't want the insanely angry gal in the pooch wagon screaming at you to get your mutt off the street during your lunch break, please consider the benefits of the siesta, instead.