Thermal Conditions for Scalar Bosons in a Curved Space Time
  The conditions that allow us to consider the vacuum expectation value of the energy-momentum tensor as a statistical average, at some particular temperature, are given. When the mean value of created particles is stationary, a planckian distribution for the field modes is obtained. In the massless approximation, the temperature dependence is as that corresponding to a radiation dominated Friedmann-like model. 
Carlos E. Laciana