You’ve gotten some good answers explaining that heat changes the density, and therefore the index of refraction of air.
Fun fact: Schlieren Imaging allows one to photograph shockwaves by relying on the same effect. As a shockwave travels through air, it creates a region of high density, which can be imaged with this technique.
I’m not sure that’s a good comparison. The kill mechanism from a neutron bomb is the deposition of ionizing radiation in the body, but the microwave radiation is non-ionizing.