  We explore a method developed in statistical physics which has been argued to
have exponentially small finite-volume effects, in order to determine the
critical temperature Tc of pure SU(3) gauge theory close to the continuum
limit. The method allows us to estimate the critical coupling betac of the
Wilson action for temporal extents up to Nt ~ 20 with < 0.1% uncertainties.
Making use of the scale setting parameters r0 and sqrt{t0} in the same range of
beta-values, these results lead to the independent continuum extrapolations Tc
r0 = 0.7457(45) and Tc sqrt{t0} = 0.2489(14), with the latter originating from
a more convincing fit. Inserting a conversion of r0 from literature
(unfortunately with much larger errors) yields Tc / LambdaMSbar = 1.24(10).
