In addition to the other factors people have mentioned, it wasn’t exactly the coolest day in Texas either - not the peak of summer like now, but it had to be in the 80s and with a merciless sun beating on him... Another consideration is that he’s got no idea where the shooter is, so running blindly isn’t the greatest idea.
He was not “running blindly”, he was walking after he quickly ran out of gas and people were directing him to the shooter. In an area such as an outdoor mall I am certain it can be difficult to pinpoint the direction the shots were coming from but you can also see blurred out images as he moved forward and I have to assume those were victims. So he knew he was getting close. He did manage to control his breathing enough when he fired his weapon.