  We determine quantum precision limits for estimation of damping constants and
temperature of lossy bosonic channels. A direct application would be the use of
light for estimation of the absorption and the temperature of a transparent
slab. Analytic lower bounds are obtained for the uncertainty in the estimation,
through a purification procedure that replaces the master equation description
by a unitary evolution involving the system and ad hoc environments. For zero
temperature, Fock states are shown to lead to the minimal uncertainty in the
estimation of damping, with boson-counting being the best measurement
procedure. In both damping and temperature estimates, sequential
pre-thermalization measurements, through a stream of single bosons, may lead to
huge gain in precision.
