  We study the nature of the finite-temperature transition of the
three-dimensional scalar chromodynamics with N_f flavors. These models are
constructed by considering maximally O(M)-symmetric multicomponent scalar
models, whose symmetry is partially gauged to obtain SU(N_c) gauge theories,
with a residual nonabelian global symmetry given by U(N_f) for N_c>2 and
Sp(N_f) for N_c=2, so that M = 2 N_c N_f. We find that their finite-temperature
transition is continuous for N_f=2 and for all values of Nc we investigated,
N_c=2,3,4. Such continuous transitions belong to universality classes related
to the global symmetry group of the theory. For N_c=2 it belongs to the
SO(5)=Sp(2)/Z_2 universality class, while for N_c>2 it belongs to the
SO(3)=SU(2)/Z_2 universality class. For N_f>2, the transition is always of
first order. These results match the predictions obtained by using the
effective Landau-Ginzburg-Wilson approach in terms of a gauge-invariant order
parameter. Our results indicate that the nonabelian gauge degrees of freedom
are irrelevant at the transition. These conclusions are supported by an
analysis of gauge-field dependent correlation functions, that are always
short-ranged, even at the transition.
