  We consider the thermal properties of a scalar field theory on curved
spacetimes. In particular, we argue for the existence in the de Sitter, Kruskal
and Rindler manifolds of a discrete spectrum of allowed temperatures (the odd
multiples of a fundamental one). For each temperature we give an explicit
construction of the relative two point function in terms of the lowest
temperature one. These results are actually valid for a wider class of static
metrics with bifurcate Killing horizons, originally studied by Sewell. Some
comments on the interpretation of our results are given.
