The damping of standing slow mode oscillations in hot (T > 6 MK) coronal loops is described in the linear limit. The effects of energy dissipation by thermal conduction, viscosity, and radiative losses and gains are examined for both stratified and nonstratified loops. We find that thermal conduction acts on the way of increasing the period of the oscillations over the sound crossing time, whereas the decay times are mostly determined by viscous dissipation. Thermal conduction alone results in slower damping of the density and velocity waves compared to the observations. Only when viscosity is added do these waves damp out at the same rate of the observed SUMER loop oscillations. In the linear limit, the periods and decay times are barely affected by gravity.