For a class of second order supersymmetric differential operators,
including the Kramers-Fokker-Planck operator of kinetic theory, we
determine the semiclassical (here the low temperature) asymptotics for the
splitting between the two lowest eigenvalues, with the first one being
0. Specifically, we consider the case when the exponent of the associated
Maxwellian has precisely two local minima and one saddle
point. The splitting is then exponentially small and is related to a
tunnel effect between the minima. We also show that the rate of the return
to equilibrium for the associated heat semigroup is dictated by the first
non-vanishing eigenvalue. This is joint work with Fr\'ed\'eric H\'erau and
Johannes Sj\"ostrand.