Decaying particles do not heat up the Universe

It is usually assumed that a massive relic species, which comes to dominate the mass density of the Universe and later decays, heats up the Universe when the age of the Universe approx. = its lifetime. It is shown that if its decay follows the usual exponential decay law, then the Universe is never reheated, rather it just cools more slowly. The evolution of the temperature and entropy are calculated. To within numerical factors of order unity, the usual estimates for the entropy increase are found to be correct. Results have implications for primordial nucleosynthesis in scenarios where a massive relic with lifetime approx. = 0.01 to 0.001 sec is present, and for baryogenesis in the new inflationary Universe scenario.