  An extension of the Keski-Vakuri, Kraus and Wilczek (KKW) analysis to black
hole spacetimes which are not Schwarzschild-type is presented. Preserving the
regularity at the horizon and stationarity of the metric in order to deal with
the across-horizon physics, a more general coordinate transformation is
introduced. In this analysis the Hawking radiation is viewed as a tunnelling
process which emanates from the non-Schwarzschild-type black hole. Expressions
for the temperature and entropy of these non-Schwarzschild-type black holes are
extracted. As a paradigm, in the context of this generalization, we consider
the Garfinkle-Horowitz-Strominger (GHS) black hole as a dynamical background
and we derive the modified temperature and entropy of GHS black hole.
Deviations are eliminated and corresponding standard results are recovered to
the lowest order in the emitted shell of energy. The extremal GHS black hole is
found to be non-``frozen'' since it is characterized by a constant non-zero
temperature. Furthermore, the modified extremality condition forbids naked
singularities to form from the collapse of the GHS black hole.
