Fluctuations of energy egr;
E
in the canonical ensemble and of temperature egr;
T
in the micro-canonical one have been evaluated theoretically as well as employing the isothermal and adiabatic molecular dynamics (MD), respectively. MD experiments were performed on Au NPs in the size range from 1.0 to 15.0 nm. As secondary results, MD data on the temperature dependence of the heat capacity of Au NPs are also obtained and analyzed. Theoretical evaluations of egr;
E
and egr;
T
satisfactory or, in some cases, very well agree with our MD results on Au NPs. We have found that egr;
T
is by about two orders of magnitude higher than egr;
E
. However, even for very small NPs (nanoclusters) consisting of 55 atoms egr;
T
is of order of 10 % only. So, a conclusion is made on applicability of both the Gibbs ensemble method and the notion of temperature in its conventional sense to NPs.