B.Barker has the right idea.
Aside from that, get a squirt bottle of water. Work slowly, only a few hammer blows at a time. As you hammer the punch through, watch which way the punch is going. Right after you pull the steel out of the fire, squirt the thin side with water so the steel cools down and the punch will move towards the hotter/thicker side as you hammer.
As my master smith used to say, "Water is a tool, not a convenience."