Multi-band signal propagation and processing play an important role in quantum communications and quantum computing. In recent years, optical nonreciprocal devices such as an optical isolator and circulator are proposed via various configurations of atoms, metamaterials, nonlinear waveguides, etc. In this work, we investigate all-optical controlled nonreciprocity of multi-band optical signals in thermal atomic systems. Via introducing multiple strong coupling fields, nonreciprocal propagation of the probe field can happen at some separated frequency bands, which results from combination of the electromagnetically induced transparency (EIT) effect and atomic thermal motion. In the proposed configuration, the frequency shift resulting from atomic thermal motion takes converse effect on the probe field in the two opposite directions. In this way, the probe field can propagate almost transparently within some frequency bands of EIT windows in the opposite direction of the coupling fields. However, it is well blocked within the considered frequency region in the same direction of the coupling fields because of destruction of the EIT. Such selectable optical nonreciprocity and isolation for discrete signals may be greatly useful in controlling signal transmission and realizing selective optical isolation functions.