The ratchet effect in heat conductions of one-dimensional Morse lattices is studied when the system is located between two averagely isothermal reserviors, of which one keeps the temperature constant and the other is periodically modulated in temperature,and their temperatures averaged over a long time are equal to each other. Unidirectional heat current can be observed when one of the heat baths is periodically modulated in temperature. The efficiency and the direction of heat conduction can be rectified and controlled by adjusting the frequency and the amplitude of the modulation. An interesting non-stationary negative thermal conductivity, i.e., a reversed heat flow against the temperature gradient, is found in an appropriate region of frequency of the modulation. A heat wave scheme in revealing the spatiotemporal behavior of the heat conduction is proposed to study the this phenomenon. The influence of the parameters of the Morse lattice on the directional heat current is investigated, and so this provides theoretical support for practical applications.