  We present a theoretical study of the impact of an electrostatic field
combined with nonresonant linearly polarized laser pulses on the rotational
dynamics of a thermal ensemble of linear molecules. We solve the time-dependent
Schr\"odinger equation within the rigid rotor approximation for several
rotational states. Using the carbonyl sulfide (OCS) molecule as a prototype,
the mixed-field orientation of a thermal sample is analyzed in detail for
experimentally accessible static field strengths and laser pulses. We
demonstrate that for the characteristic field configuration used in current
mixed-field orientation experiments, a significant orientation is obtained for
rotational temperatures below 0.7K or using stronger dc fields.
