Why are you trying to toebash the thing back into the Asteroid Belt? Obviously that's not gonna work and even the anon that mentioned diverting it probably meant something more along the lines of pushing it sideways into something else's orbit than straight-up pushing it backwards.
I have no hope of repulsing
the asteroid. I want to split
it. If you slice a spherical rock in half, you increase its surface area by no less than 25% which means that you'll increase the amount of energy dissipated as heat by that much from this alone. Also taking into consideration the shittier aerodynamics you'll not only lose even more energy, but also the descent will be slowed so that even the heat energy is wasted, every division will drastically reduce the kinetic energy of the impact. Thermal energy is hardly an issue since it'll just distribute itself across the planet and half of it will go back into space anyway.
So yes, as in the movie we want to cut the meteor into as many pieces as possible. I'd have to do some crazy calculations about the heat capacity of silicon and the expansion of its gas, the strength of silicon at space temperature and other such bullshittery to figure out whether we could shatter your fußball of death, but here is a diagram of what I'm thinking. Castle Bravo made a 2km crater and they set that off without actually trying to crack the Earth. It would have been much larger and dirtier
had they set it off underground such as by injecting the warhead via a bunker buster. By making an initial crater with a smaller warhead you could set the primary warhead deeper in the asteroid thus maximizing the energy used for expanding forces as well as putting them where they'll do the most harm. You could even synch up multiple nukes in a pattern so that you can predictably split up the asteroid. The method would be similar to how a stonemason might cut a stone: Drill a series of carefully measured holes then simultaneously drive a wedge into each hole until a clean cut is made. Only this time instead of a hammer drill you're using bunker busters and instead of wedges you're using thermonuclear warheads.