  We consider thermal effects in the propagation of gravitational waves on a
cosmological background. In particular, we consider scalar field cosmologies
and study gravitational modes near cosmological singularities. We point out
that the contribution of thermal radiation can heavily affect the dynamics of
gravitational waves giving enhancement or dissipation effects both at quantum
and classical level.These effects are considered both in General Relativity and
in modified theories like $F(R)$ gravity which can be easily reduced to
scalar-tensor cosmology. The possible detection and disentanglement of standard
and scalar gravitational modes on the stochastic background are also discussed.
