  In calculating Feynman diagrams at finite temperature, it is sometimes
convenient to isolate subdiagrams which do not depend explicitly on the
temperature. We show that, in the imaginary time formalism, such a separation
can be achieved easily by exploiting a simple method, due to M. Gaudin, to
perform the sum over the Matsubara frequencies. In order to manipulate freely
contributions which may be individually singular, a regularization has to be
introduced. We show that, in some cases, it is possible to choose this
regularization in such a way that the isolated subdiagrams can be identified
with analytical continuations of vacuum n-point functions. As an aside
illustration of Gaudin's method, we use it to prove the main part of a recent
conjecture concerning the relation which exists in the imaginary time formalism
between the expressions of a Feynman diagram at zero and finite temperature.
