A system theory approach to thermospheric modeling is developed, based upon a linearization method which is capable of preserving nonlinear features of a dynamical system. The method is tested using a large, nonlinear, time-varying system, namely the thermospheric general circulation model (TGCM) of the National Center for Atmospheric Research. We compare TGCM simulation results with results from our approximation procedure at Millstone Hill and Arecibo, two locations where there may be interest for using this approach. In the linearized version an equivalent system, defined for one of the desired TGCM output variables, is characterized by a set of response functions that is constructed from corresponding quasi-steady state and unit sample response functions. The number of functions in the set depends on the degree of nonlinearity of the original system and the desired accuracy of the approximation. Using the set of response functions, we are able to approximate time-dependent TGCM simulation results with reasonable accuracy. The linearized version of the system runs on a personal computer and produces an approximation of the desired TGCM output field height profile at a given geographic location. The approximation is obtained by performing a specialized convolution between the cross polar cap potential drop as input and the set of response functions. This enables an efficient first-order comparison between experimental data and theoretical simulations and may provide an operationally efficient means of more realistically predicting density variations for satellite ephemeris or reentry trajectory determinations during geomagnetic quiet periods as well as during magnetic storms.