Thermalization of a particle by dissipative collisions

One considers the stationary state of a test particle immersed in a homogeneous fluid in equilibrium at temperature T, undergoing dissipative collisions with the fluid particles. It is shown that the corresponding linear Boltzmann equation still possesses 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.