We present numerical methods for the numerical solution of an overdetermined symmetric hyperbolic and thermodynamically compatible (SHTC) model of compressible two-phase flows. The model has the peculiar feature that it is endowed with two entropy inequalities, one for each phase, as primary evolution equations ensuring total entropy growth. The total energy conservation law is an extra conservation law and is obtained via suitable linear combination of all other equations based on the Godunov variables also referred to as mainfield. The model describes a two-phase flows of heat conducting fluids modelled by a relaxation process, where in the stiff relaxation limit the SHTC model tends to an asymptotically reduced Baer–Nunziato-type (BN) limit with Fourier-type heat conduction. Moreover, by doing so, a unique choice for the interface velocity and the interface pressure is obtained, quantities that are usually heuristically determined in the BN model. In addition, additional lift forces in the SHTC model can be identified which are not standard in BN representation of two-phase flows. A key feature of the hyperbolic thermodynamically compatible (HTC) finite volume scheme is that it directly evolves the entropies and the energy is conserved as consequence. We show computational results for several benchmark problems in one and two space dimensions, comparing numerical results obtained for the asymptotically reduced BN limit system.