We present a switched linear system approach for modeling the complex nonlinear dynamics associated with temperature inversion occurring in thermally stratified hot water tanks. Such tanks are commonly used for thermal energy storage, particularly in low- to medium-temperature waste heat recovery applications. By separating the influence of temperature inversion from the internal heat transfer between states in the governing differential equations, we paramaterize the nonlinearity using a vector of discrete variables. This vector is then used to define the switching between a set of linear, discrete time models. The proposed switched model is validated against a reduced-order nonlinear model of the thermal energy storage and then integrated with a fuel cell model to capture the dynamics of a micro-combined heat and power system. Simulation results demonstrate the importance that temperature inversion has on the stratification dynamics which in turn has implications for control of such systems.