Elements from iron to uranium are expected to have been produced in the r-process nucleosynthesis via rapid neutron capture at elevated temperatures of the order of Giga Kelvins (GK).The network of coupled differential equations used to determine the abundance of elements thus involves nuclear reaction rates at elevated temperatures.The path of the r-process nucleosynthesis is along highly unstable nuclei and hence nuclear decay rates play an important role too.However, standard codes available for such calculations make use of terrestrial half-lives for alpha decay.Within a statistical approach and using data on excited nuclei, we find that for temperatures between 1-2 GK, the alpha decay half-lives can decrease by a few orders of magnitude as compared to the terrestrial ones.Based on these results, an estimate for the variations of the abundance of elements due to temperature-dependent half-lives is provided for a high entropy wind scenario.A model for the radioactive decay of thermally excited heavy nuclei by emitting an alpha or a light cluster such as 14 C, 20 O, or 28 Mg is also presented and applied to evaluate the less known light cluster decay rates.