  Recent results on QCD thermodynamics are presented. The nature of the T>0
transition is determined, which turns out to be an analytic cross-over. The
absolute scale for this transition is calculated. The results were obtained by
using a Symanzik improved gauge and stout-link improved fermionic action. In
order to approach the continuum limit four different sets of lattice spacings
were used with temporal extensions N_t=4, 6, 8 and 10 (they correspond to
lattice spacings a \sim 0.3, 0.2, 0.15 and 0.12 fm). The equation of state is
determined on N_t=4 and 6 lattices. The importance of the continuum limit for
different results (critical endpoint, colour superconducting phase) at
non-vanishing baryonic densities is discussed.
