Consider a de-Sitter universe with exponential expansion (cosmological constant dominated). As explained here: http://math.ucr.edu/home/baez/end.html such an universe does not tend to a thermal death, or to a 0° K state, but to a state with a constant temperature above 0 °K (prof. Baez estimates 10^-30 °K). After this temperature is reached, it will remain constant regardless of the susequent expansion of space. This is due to the fact that the cosmological horizon radiates in a similar way that observers in a Rindler space are immersed in an Unruh radiation. With my very limited knowledge about QFT, I understood qualitatively the reason for the Unruh radiation (creation and annihilation operators are defined in different ways for Minkowski and Rindler spaces, which leads to different gound states of the Hamiltonian) and I found that it depends directly on the acceleration (T = a / 2 pi). My assumption is that the same (or a similar) derivation applies for a de-Sitter universe and that the temperature does also depend on the acceleration. Correct? But then the following question raises: if the acceleration is not constant and is growing exponentially, does this mean that the temperature in a de-Sitter universe will grow due to this effect? This seams very strange to me… Thanks.