On the phase structure of lattice QCD with twisted-mass Wilson fermions at non-zero temperature

In this talk we give an overview of the 3D phase diagram of two-flavour non-zero temperature lattice QCD with twisted-mass Wilson fermions and a tree-level Symanzik-improved gauge action. We present a first feasibility study at maximal twist and, for the quenched case, we demonstrate automatic O(a)-improvement to work.