Atoms can't vibrate, but molecules can.
Heat isn't just vibrations. Heat is energy that is randomly spread among all the objects and all the ways that each object can be excited. But, the minimum vibrational energy is smaller than the minimum electronic energy, so statistically, it is more likely for the energy to randomly be in vibrational modes, since the energy likes to be as spread out as possible among all the objects.
On Earth, we are typically working with things which are at relatively low temperatures. At these low temperatures, in thermal equilibrium (after everything has settled out), it is very unlikely for any molecule to have enough energy to be in an excited electron state, but it is not unlikely to be in an excited vibrational state, because these states have low energy. (For more, see Boltzmann distribution).