  In this article we revisit the discussion of renormalons in the frame of a
scalar self-interacting $\lambda \phi^{4}$ theory in the presence of
thermomagnetic effects, i.e magnetic and thermal effects. Our results for the
evolution of the residues is now given by an explicit analytic expression,
valid for all values of temperature, without the necessity of separating the
discussion in a low- and a high temperature region analyses. We carry out the
same discussion for the case of an external constant electric field, obtaining
also in this case an analytic expression for the whole range o temperature. In
both cases, the location of the poles in the Borel plane does not change with
respect to the vacuum case. Their residues, however, acquire a dependence on
temperature and the external field. Results are presented for the evolution of
residues in the thermomagnetic and thermoelectric cases. We show a comparison
with our previous results in the thermomagnetic case, presenting also in detail
the mathematical techniques needed for our analytic expressions to be valid in
the whole range of temperature.
