  Hawking radiation of a non-asymptotically flat (NAF) 4-dimensional
spherically symmetric and static dilatonic black hole (BH) via the
Hamilton-Jacobi (HJ) method has been studied. In addition to the naive
coordinates, we have used four more different coordinate systems which are
well-behaved at the horizon. Except the isotropic coordinates, direct
computation of the HJ method leads us the standard Hawking temperature for all
coordinate systems. The isotropic coordinates render possible to get the index
of refraction extracting from the Fermat metric. It is explicitly shown that
the index of refraction determines the value of the tunneling rate and its
natural consequence, Hawking temperature. The isotropic coordinates within the
conventional HJ method produce wrong result for the temperature of the
dilatonic BH. Here, we explain how this discrepancy can be resolved by
regularizing the integral possessing a pole at the horizon.
