The present study focuses on the thermal characterization of an insulation material made from recycled textile fibers for building applications, which qualifies as a semi-transparent medium. Experimental and numerical studies have been carried out to determine the radiative flux ratio for such a recycled textile fiber-based insulation for three thicknesses (5.35 mm, 5.67 mm and 6.64 mm). The inverse method, which relies on reflection and transmission measurements using a Fourier-Transform Infrared Spectrometer coupled to an integrating sphere, has been applied along with a least squares procedure. The relevant radiative properties of recycled textile insulation material are obtained by minimizing the deviation between experimental and theoretical data. The effective thermal conductivity of the fibrous insulation is measured at room temperature by means of a fluxmeter device. The radiative thermal conductivity is estimated by implementing the Rosseland model, while phonic conductivity is derived from the effective thermal conductivity. The radiative thermal conductivity displays a very limited effect in comparison with phonic thermal conductivity; the latter varies according to thickness, which in turn is determined by fiber density and size. Phonic thermal conductivity accounts for 26% of the effective thermal conductivity and moreover constitutes a large share (74%) relative to the radiative conductivity. The maximum radiative thermal conductivity value equals 0.0102 W m−1 K−1 for a thickness of 5.67 mm, with this value dropping slightly to 0.010 W m−1 K−1 for a thickness of 6.46 mm, and to a minimum value of 0.0096 W m−1 K−1 at a 5.35-mm thickness.