A semi-analytical approximation to the solution of the radial Fourier equation describing liquid temperature dynamics in the vicinity of a spherical bubble is presented. This approximation opens a possibility to construct a computationally efficient bubble model that is flexible enough to simulate different bubble dynamics behavior like bubble growth, collapse, and oscillations. In turn, it allows development of two-pressure computer codes aiming at simulation of processes in liquid with bubbles that are important for industrial applications. The model is based on the system of ordinary differential equations (ODEs) and is presented together with results of simulations and comparison with some available experimental data. Additionally, scenarios like strong bubble parameter oscillations in largely subcooled water and abrupt liquid pressure change are considered. As respective simulations show, the latter may lead to subsequent hydrogen explosion if hydrogen–oxygen mixture is presented in the bubble. This may be important for boiling water reactor piping safety analysis.