I believe that, because no important event signalized his consulate, it has been unnoticed.
Jupiter's temple in the Capitol had not yet been dedicated; the consuls Valerius and Horatius cast lots which should dedicate it.

It fell by lot to Horatius.

Publicola departed to the war of the Veientians.

The friends of Valerius were more annoyed than they should have been, that the dedication of so celebrated a temple should be given to Horatius.[72] Having endeavoured by every means to prevent that, when all other attempts had been tried in vain, when the consul was now holding the door-post during his offering of prayer to the gods, they suddenly announce to him the shocking intelligence that his son was dead, and that his family being defiled[73] he could not dedicate the temple.

Whether he did not believe the fact, or possessed such great firmness of mind, is neither handed down for certain, nor is a conjecture easy.