Arguments based on symmetry and thermodynamics may suggest the existence of a ratchetlike lateral Casimir force between two plates at different temperatures and with broken inversion symmetry. We find that this is not sufficient, and at least one plate must be made of nonreciprocal material. This setup operates as a heat engine by transforming heat radiation into mechanical force. Although the ratio of the lateral force to heat transfer in the near field regime diverges inversely with the plates separation, d, an Onsager symmetry, which we extend to nonreciprocal plates, limits the engine efficiency to the Carnot value η_{c}. The optimal velocity of operation in the far field is of the order of cη_{c}, where c is the speed of light. In the near field regime, this velocity can be reduced to the order of ω[over ¯]dη_{c}, where ω[over ¯] is a typical material frequency.