  We investigate the effect of a variable, i.e. time-dependent, background on
the standing acoustic (i.e. longitudinal) modes generated in a hot coronal
loop. A theoretical model of 1D geometry describing the coronal loop is
applied. The background temperature is allowed to change as a function of time
and undergoes an exponential decay with characteristic cooling times typical
for coronal loops. The magnetic field is assumed to be uniform. Thermal
conduction is the dominant mechanism of cooling the hot background plasma in
the presence of an unspecified thermodynamic source that maintains the initial
equilibrium. The influence of the rapidly cooling background plasma on the
behaviour of standing acoustic (longitudinal) waves is investigated
analytically. The temporally evolving dispersion relation and wave amplitude
are derived by using the WKB theory. An analytic solution for the
time-dependent amplitude that describes the influence of thermal conduction on
the standing longitudinal (acoustic) wave is obtained by exploiting the
properties of Sturm-Liouville problems. Next, numerical evaluations further
illustrate the behaviour of the standing acoustic waves in a system with
variable, time dependent background. The results are applied to a number of
detected loop oscillations. We find a remarkable agreement between the
theoretical predictions and the observations. The cooling of the background
plasma due to thermal conduction is found to cause a strong damping for the
slow standing magneto-acoustic waves in hot coronal loops in general. Further
to this, the increase in the value of thermal conductivity leads to a strong
decay in the amplitude of the longitudinal standing slow MHD waves.
