  We investigate an important question of Hawking-like radiation as seen by an
infalling observer during gravitational collapse. Using the functional
Schrodinger formalism we are able to probe the time dependent regime which is
out of the reach of the standard approximations like the Bogolyubov method. We
calculate the occupation number of particles whose frequencies are measured in
the proper time of an infalling observer in two crucially different space-time
foliations: Schwarzschild and Eddington-Finkelstein. We demonstrate that the
distribution in Schwarzschild reference frame is not quite thermal, though it
becomes thermal once the horizon is crossed. We approximately fit the
temperature and find that the local temperature increases as the horizon is
approached, and diverges exactly at the horizon. In Eddington-Finkelstein
reference frame the temperature at the horizon is finite, since the observer in
that frame is not accelerated. These results are in agreement with what is
generically expected in the absence of backreaction. We also discuss some
subtleties related to the physical interpretation of the infinite local
temperature in Schwarzschild reference frame.
