  Let L(t) be a Levy flights process with a stability index \alpha\in(0,2), and
U be an external multi-well potential. A jump-diffusion Z satisfying a
stochastic differential equation dZ(t)=-U'(Z(t-))dt+\sigma(t)dL(t) describes an
evolution of a Levy particle of an `instant temperature' \sigma(t) in an
external force field. The temperature is supposed to decrease polynomially
fast, i.e. \sigma(t)\approx t^{-\theta} for some \theta>0. We discover two
different cooling regimes. If \theta<1/\alpha (slow cooling), the jump
diffusion Z(t) has a non-trivial limiting distribution as t\to \infty, which is
concentrated at the potential's local minima. If \theta>1/\alpha (fast cooling)
the Levy particle gets trapped in one of the potential wells.
