My fireplace has a metal firebox (3 sides) and a passive heat-o-later, which is basically a channel on either side, behind the the face. The channels have high & low vents, so the cool air is sucked in and heated as it passes the firebox. I think it works great. I can't tell you too much about the design because it was here before me. The house is about 55 years old and I imagine it is original. At one point a sweep had me concerned about rust-through but it has not been a problem.
One thing to think about: metal may conduct heat better than stone but the the stone (or brick or whatever) makes a great heat sink. If I burn wood for an evening, the stone around the firebox will still be warm the next morning. i think it is all in the design of the complete unit and I can't guess how to retrofit this.