  We report progress in our exploration of the finite-temperature phase
structure of two-flavour lattice QCD with twisted-mass Wilson fermions and a
tree-level Symanzik-improved gauge action for a temporal lattice size
N_{\tau}=8. Extending our investigations to a wider region of parameter space
we gain a global view of the rich phase structure. We identify the finite
temperature transition/crossover for a non-vanishing twisted-mass parameter in
the neighbourhood of the zero-temperature critical line at sufficiently high
\beta. Our findings are consistent with Creutz's conjecture of a conical shape
of the finite temperature transition surface. Comparing with NLO lattice chiral
perturbation theory we achieve an improved understanding of this shape.
