  We investigated the finite temperature (T) phase transition for SU(Nc) gauge
theory with Nc=4, 6, 8 and 10 at lattice spacing, a, of 1/(6T) or less. We
found that these theories have first order transitions at such small a. In many
cases we were able to find the critical couplings with precision as good as a
few parts in 10^4. We also investigated the use of two-loop renormalization
group equations in extrapolating the lattice results to the continuum, thus
fixing the temperature scale in units of the phase transition temperature, Tc.
We found that when a \le 1/(8Tc) the two-loop extrapolation was accurate to
about 1--2%. However, we found that trading Tc for the QCD scale, Lambda_MSbar,
increases uncertainties significantly, to the level of about 5--10%.
