Isn't that obvious the feet will get burned? It's full sun, it feels hot outside, in the distance ripples might even be seen above the asphalt--and yet walking is done barefoot rather than wearing some kind of shoe.
However, I consider challenging the heat as part of the summer barefoot experience, and burned soles are an expected result. They can be burned red, stinging, feeling hot, even to the point of being able to feel a pulse in the soles--as long as they did not blister. The increased heat tolerance for the next day and beyond is worth it.
Don't worry about burning the feet unless they are tingling painfully and there isn't a cooler surface or shade to find immediate heat relief. I've found that if the tingling becomes a sharp pinching water feeling then the feet have actually blistered.