It is needed for computing unimolecular reaction rates, sampling initial conditions for dynamics, studying fragmentation and radiative cooling of electrostatically trapped ions, determining thermionic electron emission of clusters beams, characterizing phase transitions in clusters, or assigning molecular species in the interstellar medium. Indeed, defining such a temperature may be helpful even for understanding the photophysics of chromophores in vacuumlike hydrophobic cavities of proteins. On the one hand, the temperature of isolated systems has been addressed pragmatically using phenomenological approaches for applied purposes. Berry and Smirnov, for instance, started from a reasonable estimate for the heat capacity of isolated clusters to derive their temperature. Another common approach has been to derive the canonical temperature for a canonical ensemble with kinetic averages equivalent to those of the microcanonical system. Andersen, Bonderup, and Hansen followed this way to derive a high-energy approximation for the molecular temperature. D'Hendecourt and co-workers estimated the properties of molecules in the interstellar medium from the observed temperature, also using an equivalent canonical approach. Most of these works, however, either do not rest on a solid statistical basis or have a limited validity domain.