Let's say you are an observer on the surface of a massive object that is collapsing to form an eventual black hole. As the object's surface approaches its own Schwarzschild radius, light from the object is increasingly redshifted, as seen by distant observers, approaching infinite redshift as the event horizon forms. Correspondingly, you on the object surface see that light from distant sources is blueshifted. Now let us assume that the top layer of the object surface remains in thermal equilibrium with the incident radiation, consisting of the cosmic microwave background plus light from other stars and galaxies. As the object shrinks closer to its Schwarzschild radius, the blueshift raises the effective temperature of the cosmic background (and other sources), so it would seem that the object's surface temperature becomes infinite! Surely this infinite temperature is unphysical, so what is the mistake in this picture I have described? Is the assumption of thermal equilibrium false? Do I misunderstand what blueshift means or how it works? Any explanation is appreciated.