Thermalization of a particle with dissipative collisions

One considers the motion of a test particle in an homogeneous fluid in equilibrium at temperature $T$, undergoing dissipative collisions with the fluid particles. It is shown that the corresponding linear Boltzmann equation still posseses a stationary Maxwellian velocity distribution, with an effective temperature smaller than $T$. This effective temperature is explicitly given in terms of the restitution parameter and the masses.