We discuss the design of the thermal analog of logic gates in systems made of a collection of nanoparticles. We demonstrate the possibility to perform NOT, OR, NOR, AND and NAND logical operations at submicrometric scale by controlling the near-field radiative heat exchanges between their components. We also address the important point of the role played by the inherent non-additivity of radiative heat transfer in the combination of logic gates. These results pave the way to the development of compact thermal circuits for information processing and thermal management.