  We present an ongoing project aimed at determining the thermodynamic Equation
of State (EoS) of quark--gluon matter from lattice QCD with two generations of
dynamical quarks. We employ the Wilson twisted mass implementation for the
fermionic fields and the improved Iwasaki gauge action. Relying on $T=0$ data
obtained by the ETM Collaboration the strange and charm quark masses are fixed
at their physical values, while the pion mass takes four values in the range
from 470 MeV down to 210 MeV. The temperature is varied within a fixed--lattice
scale approach. The values for the pseudocritical temperature are obtained from
various observables. For the EoS we show preliminary results for the pure
gluonic contribution obtained at the pion mass value 370 MeV, where we can
compare with previously obtained results with $N_f=2$ degenerate light
flavours.
