A link between horizons, imaginary time, and temperature is developed at the heuristic level first, before being made precise in the following sections with the use of Bogolyubov transformations. This leads to the derivation of the Unruh effect, which shows that an accelerated observer experiences a temperature. Analogous methods allow one to derive the phenomenon of Hawking radiation by which black holes can evaporate, and an explicit calculation of the closely related Hawking–Page transition is provided via path integral methods in which the background spacetime is also quantized. It is further shown that due to the existence of a horizon, one may in the same way associate a temperature with de Sitter spacetime. An explicit discussion of de Sitter mode functions is included, because it relates directly to the quantization of inflationary fluctuations.