In this work, we are interested in the numerical simulation of a high-speed hot jet impinging on a free liquid surface at rest by means of diffuse interface models. We first consider the case of a low-temperature subsonic jet; a 4-equation model is used on a 2D axi-symmetric setup. Turbulence is accounted for by solving the Reynolds averaged equations and using a k-ω turbulence model. Numerical results are evaluated by comparing the depth of the cavity formed in the liquid surface to the predicted values using theoretical models from the literature. We then consider the case of a high-temperature jet. We start by showing equilibrium assumption between the liquid and gas phases which is no longer valid. A 5-equation model that does not rely on this assumption is presented. Both models are compared numerically on a simplified set-up.