  The massless three dimensional Gross-Neveu-Yukawa (GNY) and
Nambu--Jona-Lasinio--Yukawa (NJLY) models at finite temperatures are analyzed
within the mean field framework considering all coupling values. When the
number of Dirac fermions is taken to be $N_f=1/4$ (GNY) and $N_f=1/2$ (NJLY)
these models relate to the supersymmetric Wess-Zumino (WZ) theory with cubic
superpotential and one superfield. In this case the results show that the
strong-weak entropy density ratio decreases from the Stefan-Boltzmann value, in
the weak limit, to $s/s_{free}=31/35$ at strong couplings. This value agrees
with the one recently obtained by applying the large-$N$ approximation to the
supersymmetric $O(N)$ WZ model with quartic superpotential and $N$ superfields.
When $N_f=0$ one obtains $s/s_{free}=4/5$ recovering, as expected, the ratio
predicted in the context of the $O(N)$ scalar model. However, contrary to the
$O(N)$ WZ model the simple Yukawa models analyzed here do not behave as CFTs
for all couplings since the conformal measure exactly vanishes only at the
extreme weak and strong limits although the speed of sound indicates that the
deviation, at intermediate couplings, appears to be rather small. By comparing
the thermal masses behavior in each case one can trace this difference as being
a consequence that in the GNY/NJLY case the fermionic mass vanishes for all
couplings while within the $O(N)$ WZ it only vanishes at the weak and strong
limits. On the other hand, the Yukawa bosonic dimensionless masses display a
more universal behavior decreasing from $2 \ln [(1+\sqrt{5})/2]$, at infinite
coupling, to zero (at vanishing coupling).
