  The dynamics of an active, finite-size and immiscible impurity in a dilute
quantum fluid at finite temperature is characterized by means of numerical
simulations of the projected Gross--Pitaevskii equation. The impurity is
modeled as a localized repulsive potential and described with classical degrees
of freedom. It is shown that impurities of different sizes thermalize with the
fluid and undergo a stochastic dynamics compatible with an Ornstein--Uhlenbeck
process at sufficiently large time-lags. The velocity correlation function and
the displacement of the impurity are measured and an increment of the friction
with temperature is observed. Such behavior is phenomenologically explained in
a scenario where the impurity exchanges momentum with a dilute gas of thermal
excitations, experiencing an Epstein drag.
