Coog
Burning Hunk
Perhaps a bit heavy on the theatrics, to teach our boy once he was mobile that the stove was hot and dangerous, I pretended to touch it, then dropped to the ground howling. He got it and never willingly went for the stove. He did trip once and grazed the stove on his way down. Fast forward a couple years and a new house and an additional child, we do protect our insert, which happens to reside in the play room. (Good planning from great parents.) The protection is not only for the kids, but also for all the random toys that could find their way near the stove.
edit: taking a closer look at OP's hearth (very beautiful, btw), I'd definitely find a way to protect the kiddos from the stone edge. That's always been my biggest fear, those sharp edges. And, while maybe not the best recommendation, we picked up the cheapest grate we could find at Box DIY to protect our stove.
Yes, the sharp edges are a greater concern for me than the hot surface. Watch the little ones slam their heads on one of those sharp edges, big ouchy.