Frenkel-Kontorova (FK) lattices with a coupling displacement was investigated.Through simplifying the model, we derived analytical expression of thermal current of the system in the overdamped case.By means of numerical calculations, the results indicate that: (i) As the coupling displacement equals to zero, temperature oscillations of the heat baths linked with the lattices can control magnitude and direction of the thermal current;(ii) Whether there is a temperature bias or not, the thermal current oscillates periodically with the coupling displacement, whose amplitudes become greater and greater;(iii) As the coupling displacement is not equal to zero, the thermal current monotonically both increases and decreases with temperature oscillation amplitude of the heat baths, dependent on values of the coupling displacement;(iv) The coupling displacement also induces non-monotonic behaviors of the thermal current with respect to spring constant of the lattice and coupling strength of the lattices;(v) These dynamical behaviors comes from the interaction of the coupling displacement with periodic potential of the FK lattices.Our results have the implication that the coupling displacement between lattices plays a crucial role in the control of heat current.