  We consider a model of a dynamical Lorentz gaz : a single particle is moving
in $\mathbb{R}^d$ through an array of fixed an soft scatterers each possessing
an internal degree of freedom coupled to the particle. Assuming the initial
velocity is sufficiently high and modelling the parameters of the scatterers as
random variables, we describe the evolution of the kinetic energy of the
particle by a Markov chain for which each step corresponds to a collision. We
show that the momentum distribution of the particle approaches a
Maxwell-Boltzmann distribution with effective temperature $T$ such that $k_BT$
corresponds to an average of the scatterers' kinetic energy.
