  We study the dynamical mass generation in Pseudo Quantum Electrodynamics
(PQED) coupled to the Gross-Neveu (GN) interaction, in (2+1) dimensions, at
both zero and finite temperatures. We start with a gapless model and show that,
under particular conditions, a dynamically generated mass emerges. In order to
do so, we use a truncated Schwinger-Dyson equation, at the large-N
approximation, in the imaginary-time formalism. In the instantaneous-exchange
approximation (the static regime), we obtain two critical parameters, namely,
the critical number of fermions $N_c(T)$ and the critical coupling constant
$\alpha_c(T)$ as a function of temperature and of the cutoff $\Lambda$, which
must be provided by experiments. In the dynamical regime, we find an analytical
solution for the mass function $\Sigma(p,T)$ as well as a zero-external
momentum solution for $p=0$. We compare our analytical results with numerical
tests and a good agreement is found.
