  We review two definitions of temperature in statistical mechanics, $T_B$ and
$T_G$, corresponding to two possible definitions of entropy, $S_B$ and $S_G$,
known as surface and volume entropy respectively. We restrict our attention to
a class of systems with bounded energy and such that the second derivative of
$S_B$ with respect to energy is always negative: the second request is quite
natural and holds in systems of obvious relevance, i.e. with a number $N$ of
degrees of freedom sufficiently large (examples are shown where $N \sim 100$ is
sufficient) and without long-range interactions. We first discuss the basic
role of $T_B$, even when negative, as the parameter describing fluctuations of
observables in a sub-system. Then, we focus on how $T_B$ can be measured
dynamically, i.e. averaging over a single long experimental trajectory. On the
contrary, the same approach cannot be used in a generic system for $T_G$, since
the equipartition theorem may be spoiled by boundary effects due to the limited
energy. These general results are substantiated by the numerical study of a
Hamiltonian model of interacting rotators with bounded kinetic energy. The
numerical results confirm that the kind of configurational order realized in
the regions at small $S_B$, or equivalently at small $|T_B|$, depends on the
sign of $T_B$.
