  We compute the nonzero temperature free energy up to the order g^6 \ln(1/g)
in the coupling constant for vector like SU(N) gauge theories featuring matter
transforming according to different representations of the underlying gauge
group. The number of matter fields, i.e. flavors, is arranged in such a way
that the theory develops a perturbative stable infrared fixed point at zero
temperature. Due to large distance conformality we trade the coupling constant
with its fixed point value and define a reduced free energy which depends only
on the number of flavors, colors and matter representation.
  We show that the reduced free energy changes sign, at the second, fifth and
sixth order in the coupling, when decreasing the number of flavors from the
upper end of the conformal window. If the change in sign is interpreted as
signal of an instability of the system then we infer a critical number of
flavors. Surprisingly this number, if computed to the order g^2, agrees with
previous predictions for the lower boundary of the conformal window for
nonsupersymmetric gauge theories. The higher order results tend to predict a
higher number of critical flavors. These are universal properties, i.e. they
are independent on the specific matter representation.
