  We show that the Mellin summation technique (MST) is a well defined and
useful tool to compute loop integrals at finite temperature in the
imaginary-time formulation of thermal field theory, especially when interested
in the infrared limit of such integrals. The method makes use of the Feynman
parametrization which has been claimed to have problems when the analytical
continuation from discrete to arbitrary complex values of the Matsubara
frequency is performed. We show that without the use of the MST, such problems
are not intrinsic to the Feynman parametrization but instead, they arise as a
result of (a) not implementing the periodicity brought about by the possible
values taken by the discrete Matsubara frequencies before the analytical
continuation is made and (b) to the changing of the original domain of the
Feynman parameter integration, which seemingly simplifies the expression but in
practice introduces a spurious endpoint singularity. Using the MST, there are
no problems related to the implementation of the periodicity but instead, care
has to be taken when the sum of denominators of the original amplitude
vanishes. We apply the method to the computation of loop integrals appearing
when the effects of external weak magnetic fields on the propagation of scalar
particles is considered.
