Radiation damage of self-assembled monolayers, which are prototypes of thin organic layers and highly organized biological systems, shows a strong dependence on temperature. Two limiting cases could be identified. Reactions involving transport of single atoms and small fragments proceed nearly independent of temperature. Reactions requiring transport of heavy fragments are, however, efficiently quenched by cooling. We foresee the combined use of temperature and irradiation by electrons or photons for advanced tailoring of self-assembled monolayers on surfaces. In addition, our results have direct implications for cryogenic approaches in advanced electron and x-ray microscopy and spectroscopy of biological macromolecules and cells.