The ability to forecast system conditions is integral to the definition and functionality of digital twins. While forecasting methods have been explored for use in digital twin systems, the integration of feedback mechanisms for real-time forecasting and in-situ decision-making in DC microgrids has not been extensively investigated. This research develops a modular forecasting framework tailored for digital twins in DC microgrids to enable real-time monitoring, online forecasting, and decision-making. DC microgrids, characterized by dynamic load variations, benefit from advanced predictive capabilities to maintain stability and operational efficiency. The proposed digital twin-based forecasting framework addresses these challenges by providing real-time predictive insights based on dynamic system conditions and a forecasting window defined by a decision-maker, facilitating proactive management strategies. Leveraging real-time sensor data, the digital twin forecasts system behavior under varying load conditions, enabling proactive management through real-time decision-making within operational constraints. As a proof of concept, the framework incorporates an electro-thermal digital twin designed to manage power flow based on thermal constraints in power distribution cables. Experimental validation using a simplified three-bus DC microgrid testbed demonstrates the effectiveness of the framework in enabling timely adjustments to power flows and preventing thermal overloads.