This study is a part of the on-going research at Loughborough University, UK, on finite element (FE) simulations of ultrasonically assisted turning (UAT) coupled with hot machining processes. In UAT, vibration is superimposed on the cutting tool movement, resulting in several advantages of the process, especially in machining of high-strength engineering materials. Direct experimental studies of machining processes are expensive and time consuming, especially when a wide range of machining parameters affects, complex thermo-mechanical high-deformation processes in machined materials. In recent years, a use of mathematical simulations and, in particular, FE techniques has gained prominence in the research community. These techniques provide an accurate and efficient modelling paradigm for machining processes. In the present work, thermo-mechanically coupled three-dimensional FE models of conventional, ultrasonically assisted turning and a new hybrid turning technique called hot ultrasonically assisted oblique turning for a case of titanium alloy are presented. A nonlinear temperature-sensitive material behaviour is incorporated in our numerical simulations based on the results of the split-Hopkinson pressure bar tests. The simulation results obtained at different cutting conditions are compared to elucidate main deformation mechanisms responsible for the observed changes in the material's responses to various cutting techniques.