  We extend our previous study [Phys. Lett. B643 (2006) 46] of the cross-over
temperatures (T_c) of QCD. We improve our zero temperature analysis by using
physical quark masses and finer lattices. In addition to the kaon decay
constant used for scale setting we determine four quantities (masses of the
\Omega baryon, K^*(892) and \phi(1020) mesons and the pion decay constant)
which are found to agree with experiment. This implies that --independently of
which of these quantities is used to set the overall scale-- the same results
are obtained within a few percent. At finite temperature we use finer lattices
down to a <= 0.1 fm (N_t=12 and N_t=16 at one point). Our new results confirm
completely our previous findings. We compare the results with those of the
'hotQCD' collaboration.
