  We consider the minimal version of an extension of the standard electroweak
model based on the $SU(3)_c \times SU(3)_L \times U(1)_X$ gauge symmetry (the
3-3-1 model). We analyze the most general potential constructed from three
scalars in the triplet representation of $SU(3)_L$, whose neutral components
develop nonzero vacuum expectation values, giving mass for all the model's
massive particles. {}For different choices of parameters, we obtain the
particle spectrum for the two symmetry breaking scales: one where the $SU(3)_L
\times U(1)_X$ group is broken down to $SU(2)_L\times U(1)_Y$ and a lower scale
similar to the standard model one. Within the considerations used, we show that
the model encodes two first-order phase transitions, respecting the pattern of
symmetry restoration. The last transition, corresponding to the standard
electroweak one, is found to be very weak first-order, most likely turning
second-order or a crossover in practice. However, the first transition in this
model can be strongly first-order, which might happen at a temperature not too
high above the second one. We determine the respective critical temperatures
for symmetry restoration for the model.
