By synthesizing stock-flow consistent models, input-output models, and aspects of ecological macroeconomics, a method is developed to simultaneously model monetary flows through the financial system, flows of produced goods and services through the real economy, and flows of physical materials through the natural environment. This paper highlights the linkages between the physical environment and the economic system by emphasizing the role of the energy industry. A conceptual model is developed in general form with an arbitrary number of sectors, while emphasizing connections with the agent-based, econophysics, and complexity economics literature. First, we use the model to challenge claims that 0% interest rates are a necessary condition for a stationary economy and conduct a stability analysis within the parameter space of interest rates and consumption parameters of an economy in stock-flow equilibrium. Second, we analyze the role of energy price shocks in contributing to recessions, incorporating several propagation and amplification mechanisms. Third, implied heat emissions from energy conversion and the effect of anthropogenic heat flux on climate change are considered in light of a minimal single-layer atmosphere climate model, although the model is only implicitly, not explicitly, linked to the economic model.