  We illustrate how to apply modern effective field theory techniques and
dimensional regularization to factorize the various scales which appear in
non-relativistic bound states at finite temperature. We focus here on the
simplest case: the hydrogen atom. We discuss in detail the interplay of the
hard, soft and ultrasoft scales of the non-relativistic system at zero
temperature with the additional scales induced at finite temperature. We also
comment on the implications of our results for heavy quarkonium bound states in
the quark gluon plasma.
