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We introduce a calculation, based on purely topological reasoning, of theglobal equilibrium Hawking temperature of the Schwarzschild-de Sitterspacetime, where a Schwarzschild black hole horizon coexists with a de Sittercosmological horizon. Our method is based on the careful calculation of theEuler characteristic of the total system, showing that this quantity completelydetermines the thermodynamical features of the system. The method is universaland can be applied to any structure possessing multiple horizons in generalrelativity.

Global Hawking Temperature of Schwarzschild-de Sitter Spacetime: a Topological Approach