We apply the theory developed in Farinella and
Vokrouhlick\'y (1996) for the thermal force effects affecting the
motion of LAGEOS--type artificial satellites to the specific case of
the the so--called Yarkovsky--Rubincam effect, due to anisotropic
heating of the satellite's surface by the Earth's infrared radiation.
This theory allows us to remove the usual assumption of a fast
rotational motion of the satellite, so as to allow for a misalignment
between the direction of the thermal force and the spin axis. When
applied to the LAGEOS satellite, which has been strongly despun by
magnetic torques since its launch in 1976, our theory shows that in
the next decade the orbital perturbations associated with the
Yarkovsky--Rubincam effect will become much different than
those predicted by the simple rapid--rotation approach. This is the
case both for the drag--like effect causing a semimajor axis decay,
and for the inclination changes.
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