We analyze the control of field-free molecular orientation at high temperature by use of a two-color laser bipulse strategy proposed in Zhang et al. [Phys. Rev. A 83, 043410 (2011)]. A general study shows that there exist two types of linear molecules for which a different mechanism has to be used. For molecules with a large hyperpolarizability, a monochromatic laser pre-pulse is applied before the two-color laser pulse at a time close to the rotational period T r , while for molecules with a small hyperpolarizability, the optimal delay is found close to T r /4 or 3T r /4. We extend this analysis to the case of a 2 molecule such as NO where a similar control strategy can be derived. These control processes are robust against temperature effects.