The economic engineering group at the DCSC uses Newtonian and analytical mechanics to model economic systems but makes no use of thermodynamics. The introduction of thermodynamics to the economic engineering framework would increase the extent of analysis and interpretation of economic systems in economic engineering. In this thesis the foundations of the thermodynamics of economic engineering are developed in order to include thermodynamic modeling of economic systems in the field of economic engineering. After the development of the thermodynamics of economic engineering theory, the theory is applied to analyze economic growth, factor productivity, and the value of a business. An axiomatic approach is taken to derive economic analogs to thermodynamic concepts. The meaning of an axiomatic approach is that these economic-thermodynamic analogs are developed in a logical order, e.g., the economic analog to temperature is not introduced before developing the economic analog to the first law. Key analogs between economics and thermodynamics are established in this thesis that include but are not limited to two fundamental economic laws, work as an expenditure, heat as an expense, temperature as a price level, and entropy as a quantity referred to as human capital in the thesis. By deriving key analogs, the thesis establishes the foundational principles of thermodynamics within economic engineering. Utilizing the theory of the thermodynamics of economic engineering results in applications to economic growth. Empirical growth accounting is modeled by the fundamental thermodynamic relationship. A relationship between linear production functions and Cobb-Douglas type production functions is shown by analyzing the productivity of an economy. Furthermore, a method to evaluate the worth of a business is created by determining the business' total potential earnings. Additionally, the thesis shares a vision of how to include thermodynamics within a control engineering framework. A higher-dimensional energy-based approach to model dynamical systems offers a way forward to include thermodynamic energy and entropy within control formalisms. Such a framework would account for availability and heat buildup in controlled dynamical systems. One potential application is to account for the heat build up that occurs in integrated circuits.