It is well known that the heat flux constitutive model of Jeffrey's type heat transport equation yields various modes of thermal energy transport. The significance of varying a given parameter “K” in the equation starting from zero and the sequence of events describing the hyperbolic (propagative / non-Fourier) wave nature of the thermal energy transport through a mildly hyperbolic transition to a fully parabolic (diffusive / Fourier) is well described in the earlier works. Based on the Taylor's series expansion, this paper interprets the Jeffrey's type heat transport equation from strategic computational method point of view so as to incorporate the parameter “K” as the time difference in the series expansion of the temperature in time at a given spatial point. This paper not only leads to better understanding of the parameter “K” as the time lag between the temperature gradient as the driving potential and its response the heat flux, but also transforms the Jeffrey's thermal model into a computationally advantageous form similar to that of Fourier's thermal model. This paper is the introducer to the series of research works carried out in the computational methods for characterizing and resolving Jeffrey's thermal problems culminating to a most power full numerical scheme in CFD, the Flow field Dependent Variation (FDV) method