What korjik said is correct.

I think where your confusion is coming from, czeslaw, is that you think a neutron star has to radiate out it's excess kinetic energy in order to collapse into a black hole. However, kinetic energy isn't what's keeping a neutron star up in the first place. A neutron star is no longer undergoing nuclear fusion, and so isn't producing any more of it's own internal energy. And while the heat generated from it's collapse is a lot, it's nowhere near enough energy to balance the inward pull of gravity. The only thing that is strong enough is the neutron degeneracy pressure, like korjik said. Once that is overcome the star simply collapses, without the star needing to radiate anything else.

Since the star doesn't need to radiate anything else to form a black hole, the fact that hawking radiation is so miniscule won't have an effect on it's collapse.