  We introduce the Friedrichs model at finite temperature which is one- and
zero-particle restriction of spin-boson in the rotating wave approximation and
obtain the population of the excited state for this model. We also consider the
oscillator interacting with bosonic thermal bath in the rotating wave
approximation and obtain dynamics of mean excitation number for this
oscillator. Both solutions are expressed in terms of integrals of
zero-temperature solutions with correspondent correlation functions.
