In the Bergman-Milton spectral representation for the effective dielectric constant of a composite all relevant geometric information is captured in a spectral function that is independent of material properties. We present numerical simulations of the reflectance of a model two component composite, where both components have temperature-dependant dielectric resonances, and show that the spectral function can be extracted from the data. The same spectral function is obtained from simulation data corresponding to different temperatures but the resolution depends on the width of the resonance line and is greatest at low-temperatures.