  We introduce a calculation, based on purely topological reasoning, of the
global equilibrium Hawking temperature of the Schwarzschild-de Sitter
spacetime, where a Schwarzschild black hole horizon coexists with a de Sitter
cosmological horizon. Our method is based on the careful calculation of the
Euler characteristic of the total system, showing that this quantity completely
determines the thermodynamical features of the system. The method is universal
and can be applied to any structure possessing multiple horizons in general
relativity.
