  The semi-classical derivation of Hawking radiation for axially symmetric,
stationary spacetimes with a Killing horizon is examined following the recent
quasi-classical tunneling analysis and a simple formula is found for the
inverse Hawking temperature $\beta = 1/T_H$. The formula is invariant under
canonical transformations and is shown to be equivalent to the integral of a
closed differential 1-form around the horizon enclosing a pole. The Hawking
temperature is then given in terms of the winding number in the first homotopy
group of the torus formed from the compactified imaginary parts of the
analytically continued radial and time variables.
