Consider a free electron gas in a confining potential and a magnetic field in
arbitrary dimensions. If this gas is in thermal equilibrium with a reservoir at
temperature $T >0$, one can study its orbital magnetic response (omitting the
spin). One defines a conveniently ``smeared out'' magnetization $M$, and the
corresponding magnetic susceptibility $\chi$, which will be analyzed from a
semiclassical point of view, namely when $\hbar$ (the Planck constant) is small
compared to classical actions characterizing the system. Then various regimes
of temperature $T$ are studied where $M$ and $\chi$ can be obtained in the form
of suitable asymptotic $\hbar$-expansions. In particular when $T$ is of the
order of $\hbar$, oscillations ``\`a la de Haas-van Alphen'' appear, that can
be linked to the classical periodic orbits of the electronic motion.