We investigate the propagation of MHD waves in a homogenous, magnetized plasma in a weakly stratified atmosphere, representing hot coronal loops. In most of earlier studies a time-independent equilibrium is considered. Here we abandon this restriction and allow the equilibrium to develop as function of time. In particular, the background plasma is assumed to be cooling due to thermal conduction. The cooling is assumed to be on a time scale greater than the characteristic travel times of the perturbations. We investigate the influence of cooling of the background plasma on the properties of magneto-acoustic waves. The MHD equations are reduced to a 1-D system modelling magneto-acoustic modes progressing along a dynamically cooling coronal loop. A time dependent dispersion relation which describes the propagation of the magneto-acoustic waves is derived by using the WKB theory. An analytic solution for the time-dependent amplitude of waves is obtained and the method of characteristics is used to find an approximate analytical solution. Numerical calculations are applied to the analytically derived solutions to obtain further insight into the behavior of the MHD waves in a system with variable, time-dependent background. The results show that there is a strong damping of MHD waves that can be linked to the widely observed damping of hot coronal loop oscillations. The damping also appears to be independent of position along the loop. Studies of MHD wave behaviour in time-dependent background seem to be a fundamental and very important next step in developing MHD wave theory applicable to a wide range in solar physics.