The Hartle-Hawking method of deriving black hole radiance (the “Hawking Process”) has been extended to non-asymptotically flat de Sitter spacetime by Gibbons and Hawking. They derive a thermal spectrum of radiation detectable by suitable observers. We extend this work to Taub-Nut spacetime and a related and more physical spacetime constructed from it by Siklos by complex analytic continuation and unwrapping. Suitable observers are found to detect thermal spectra in these two spacetimes as well.