In this talk I will discuss the main problems in building a consistent AQFT in Schwarzschild spacetime for a thermal system ruled by an interacting and massive scalar field, extending the methods and the results of Fredenhagen and Lindner. In particular I will focus on the decay rate of the vacuum two-point function along spatial directions, showing that, despite the non vanishing curvature, a KMS state for the interacting system can be constructed. Eventually I will comment on the applicability of this scheme to generic, stationary, asymptotically Minkowskian spacetimes. Joint work with Claudio Dappiaggi.