Earth radiation budget instruments are devices designed to study global climate change. These instruments use telescopes embarked on low-earth-orbit satellites to measure Earth emitted and reflected solar radiation. Radiation is sensed as temperature changes caused by radiation absorbed during scans of the earth on a delicate gold-black coated detector. This work is part of a larger effort to develop an end-to-end dynamic electro-thermal model, based on first-principles, for the next generation of earth radiation budget instruments, the Radiation Budget Instrument (RBI). A primary objective of this effort is to develop a numerical model of the detector to be used on RBI. Specifically, the sensor model converts radiation arriving at the detector, collimated and focused through telescopes, into sensible heat; thereby producing a voltage. A mathematical model characterizing this sensor is developed. Using a MATLAB algorithm, an implicit finite-volume scheme is implemented to determine the model solution. Model parameters are tuned to replicate experimental data using a robust parameter estimation scheme. With these model parameters defined, the electro-thermal sensor model can be used, in conjunction with the remaining components of the end-to-end model, to provide insight for future interpretation of data produced by the RBI. / Master of Science