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It is the author's premise that it is possible to gain a better understanding of systems theory and the modeling process by examining the anomalous heat flow model. This examination suggests new areas for research in systems theory. The product of the through and across variables does not yield power, an inductive component does not exist, and the through variable is not measured in the usual way. A closer study of these anomalies has broad implications for the methods of systems theory in general. Among these implications are (1) for every physical phenomenon there is a variable set that provides all of the generic characteristics; (2) every physical system has an alternate formulation using energy flow rate as the `through variable'; (3) physical systems that would normally be modeled using discrete variable sets can be united in a single model; and (4) methodological advances are required in order to deal with random diffusion processes such as heat flow. Further, some insight is gained into the effect of a macroscopic versus a microscopic viewpoint in model building.