  Through a detailed investigation of the $SU(3)$ gauge theory at finite
temperature on lattices of various size we can control finite lattice cut-off
effects in bulk thermodynamic quantities. We calculate the pressure and energy
density of the $SU(3)$ gauge theory on lattices with temporal extent $N_\tau =
4$, 6 and 8 and spatial extent $N_\sigma =16$ and 32. The results are
extrapolated to the continuum limit. We find a deviation from ideal gas
behaviour of (15-20)\%, depending on the quantity, even at temperatures as high
as $T\sim 3T_c$. A calculation of the critical temperature on lattices with
temporal extent $N_\tau = 8$ and 12 and the string tension on $32^4$ lattices
at the corresponding critical couplings is performed to fix the temperature
scale. An extrapolation to the continuum limit yields $T_c/\sqrt{\sigma} =
0.629(3)$.
