  We establish a connection between the trace anomaly and a thermal radiation
in the context of the standard cosmology. This is done by solving the covariant
conservation equation of the stress tensor associated with a conformally
invariant quantum scalar field. The solution corresponds to a thermal radiation
with a temperature which is given in terms of a cut-off time excluding the
spacetime regions very close to the initial singularity. We discuss the
interrelation between this result and the result obtained in a two-dimensional
schwarzschild spacetime.
