  Hawking radiation is studied for arbitrary scalars, fermions, and spin-1
bosons, using a tunneling approach, to every order in $\hbar$ but ignoring
back-reaction effects. It is shown that the additional quantum terms yield no
new contribution to the Hawking temperature. Indeed, it is found that the limit
of small $\hbar$ in the standard quantum WKB approximation is replaced by the
near-horizon limit in the gravitational WKB approach.
