That’s a lot of damage.
A few dozen hydrogen bombs have been set off in the atmosphere, and many more underground. They generated temperatures of the same order of magnitude of those you are concerned about, on the ground, high in the atmosphere, and under the earth.
The idea that the would touch off an atomic conflagration of the atmosphere was analyzed in some detail by Leo Szilard, Hans Bethe, Edward Teller, and others, back in the late '40s and early '50s. They predicted no such phenomenon would occur (actually they told President Truman that the probability was very small). There was in fact no such ignition of the atmosphere. Is that not sufficient evidence for you?
Yes that is sufficient for me.
What would be the damage radius of such a heat outbreak?
Those islands where H-bombs were tested , they were utterly destroyed as well as ships surrounding them. That was purely from the heat, not the gamma radiation afterwards. Loooks to me about a 2-3 mile radius.