If I understand correctly, you want to measure the emissivity of the plastic disc with metallic thin film at room temperature. You can use a FTIR spectrometer to measure the reflectance spectrum (R) of the sample, and then you can get the absorptance (A) from A=1-R-T, where transmission should be zero due to the thick structure. According to the Kirchhoff's Law, the emittance at a certain wavelength is equal to the absorptance at that wavelengths. Then you can get the emittance.