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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 Nt = 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 zerotemperature
critical line at sufficiently high b . Our findings are consistent with Creutz’s conjecture
of a conical shape of the finite temperature transition surface. Comparing with NLO lattice
cPT we achieve an improved understanding of this shape.