  We prove that for a combined system of classical and quantum particles, it is
possible to write a dynamics for the classical particles that incorporates in a
natural way the Boltzmann equilibrium population for the quantum subsystem. In
addition, these molecular dynamics do not need to assume that the electrons
immediately follow the nuclear motion (in contrast to any adiabatic approach),
and do not present problems in the presence of crossing points between
different potential energy surfaces (conical intersections or spin-crossings).
A practical application of this molecular dynamics to study the effect of
temperature in molecular systems presenting (nearly) degenerate states - such
as the avoided crossing in the ring-closure process of ozone - is presented.
