Give your vet a call and see what he thinks.
From what it sounds like, you may want to get him on an anhidrosis supplement, and before you walk him, hose his chest, neck and juggular vein, and then walk him.
It sounds about the same as my mini would do before we got him on his anhidrosis supplement. He would breath super hard, and heart rate way up, just from grazing in the heat. Also, no sweat whatsoever. He has since, had no more problems with the heat.