  In vacuum, the world-line formalism is an efficient tool for calculating
observables in the presence of arbitrary constant external fields. The natural
frame of this formalism is the Euclidean space. At finite temperature the
analytic continuation to Minkowski space is a subtle task. We study the two
point function in scalar QED, and we figure out the problem of analytic
continuation giving a possible solution for it. We also show, in contrast to
what was claimed in the literature, that a translationally invariant world-line
Green's function could be used at finite temperature.
