  We reassess the problem of renormalization in finite temperature field theory
(FTFT). A new point of view elucidates the relation between the ultraviolet
divergences for T=0 and $T \not= 0$ theories and makes clear the reason why the
ultraviolet behavior keeps unaffected when we consider the FTFT version
associated to a given quantum field theory (QFT). The strength of the
derivation one lies on the H\"ormander's criterion for the existence of
products of distributions in terms of the wavefront sets of the respective
distributions. The approach allows us to regard the FTFT both imaginary and
real time formalism at once in a unified way in the contour ordered formalism.
