Forecasting the thermal behavior of flexible heating assets is essential for real-time energy management in heating systems. While thermal dynamics are complex, the optimization algorithms within EMS require low-order models with minimal computational load to make rapid, real-time decisions. To bridge this gap, this study develops and validates low-order, data-driven models for a heat pump, an electric boiler and the indoor temperature of an office building. These models are designed for integration into the Digital Twin EMS of an industrial site. The e-boiler is characterized by its efficiency frequency distribution, which is centered at 85%, allowing it to be represented by a constant value. For the heat pump, a third-order polynomial captures how the COP depends on the outdoor temperature with a MAE of COP = 0.41. Indoor temperature dynamics are described with a discretized first-order model whose constant parameters are identified via four-minute nighttime regression; daytime disturbances are estimated either from training data or a three-day rolling profile. The developed indoor-temperature dynamic model predicts office temperatures with an overall MAE below a 0.3 \(^{\circ }\) C threshold, which humans cannot perceive. The resulting low-order models are suitable for integration into model-predictive algorithms that schedule the operation of the heating system.