One considers the stationary state of a test particle immersed in a homogen
eous fluid in equilibrium at temperature T, undergoing dissipative collisio
ns with the fluid particles. It is shown that the corresponding linear Bolt
zmann equation still possesses a stationary Maxwellian velocity distributio
n, with an effective temperature smaller than T. This effective temperature
is explicitly given in terms of the restitution parameter and the masses.