  A method for the computation of the radiative momentum transfer in the
Pioneer 10 & 11 spacecraft due to the diffusive and specular components of
reflection is presented. The method provides a reliable estimate of the thermal
contribution to the acceleration of these deep space probes and allows for a
Monte-Carlo analysis from which an estimate of the impact of a possible
variability of the parameters. It is shown that the whole anomalous
acceleration can be explained by thermal effects. The model also allows one to
estimate the expected time evolution of the acceleration due to thermal
effects. The issue of thermal conduction between the different components of
the spacecraft is discussed and confirmed to be negligible.
