  We present numerical results for the phase diagram of lattice QCD at finite
temperature in the formulation with twisted mass Wilson fermions and a
tree-level Symanzik-improved gauge action. Our simulations are performed on
lattices with temporal extent N_\tau=8, and lattice coupling \beta ranging from
strong coupling to the scaling domain. Covering a wide range in the space
spanned by the lattice coupling \beta and the hopping and twisted mass
parameters \kappa and \mu, respectively, we obtain a comprehensive picture of
the rich phase structure of the lattice theory. In particular, we verify the
existence of an Aoki phase in the strong coupling region and the realisation of
the Sharpe-Singleton scenario at intermediate couplings. In the weak coupling
region we identify the phase boundary for the physical finite temperature phase
transition/crossover. Its shape in the three-dimensional parameter space is
consistent with Creutz's conjecture of a cone-shaped thermal transition
surface.
