  We illustrate how to apply modern effective field theory techniques and
dimensional regularization to factorise the various scales which appear in QED
bound states at finite temperature. We focus here on the muonic hydrogen atom.
Vacuum polarization effects make the physics of this atom at finite temperature
very close to that of heavy quarkonium states. We comment on the implications
of our results for these states in the quark gluon plasma. In particular, we
estimate the effects of a finite charm quark mass in the dissociation
temperature of bottomonium.
