Since the photon that strikes it contains energy, when it is absorbed that energy is transferred to the atom. This can be used to add motion to the atom, or to push an electron to a higher energy orbit. In the latter case the electron may drop back at some later date and release a photon (fluoresce) but this photon will be of lower energy than the first (thank you 2nd law of thermodynamics)

You know, the definition of temperature gecomes very tricky when you are speaking of single molecules or atoms. Temperature is a mass quality, referring to averages of the relative motions of molecules in a gas or substance. 

Referring to "temperature" of a single atom becomes much like referring to the kinetic energy of a body. There are other aspects too, such as the excitation of its electrons, but in such matters one has to be very careful of how you define what exactly you are talking about if you want to be sure of talking sense.

Just as a PS, some of the "vibration" involved is of the nucleus and the orbital electrons relative to each other. Incidentaly, at really, really far cryogenic temperatures the two are not well coupled, and this makes it difficult to get close to absolute zero, because you cannot do much to cool the nucleus by cooling the electrons beyond a certain degree, for example.

I think a single atom without others around it would not "swing" but rather fly in one direction all the time until it bangs into something (there is no perfect vacuum, is there?). And we would define the "temperature" not by the speed of its swinging but by the speed of its moving.

And, as has been said, the only way for heat to an atom with no neighbors is by radiation, that is, photons.