  The free energy density of the SU(3) gauge theory at temperatures T/T_c =
4/3, 3/2 and 2 is calculated on lattices with temporal extent as small as N_t =
2, 3 and spatial extent N_s = 4 N_t using parametrized fixed point actions.
Although cut-off effects are seen, they are hugely suppressed with respect to
Wilson and Symanzik-improved actions and at N_t = 3 there is already a good
agreement with the continuum limit as extrapolated from the results with the
Wilson action at N_t = 6 and 8.
