Biological warfare question

I saw a woman on MSNBC a couple of days ago talking about how some old Soviet ICBMS were fitted with tops filled with anthrax or smallpox. This may sound stupid, but wouldn’t the bacteria or virus be killed when the missle exploded?

They could detonate a small concussion type explosive while the missile was still airborn…so that the dust would be released to drift down and around.
Don’t imagine a scenario where the whole missle goes crashing into a building with a huge fireball upon impact.