In this work, biobased rigid polyurethane foams (PUFs) were developed with the aim of achieving thermal and fireproofing properties that can compete with those of the commercially available products. First, the synthesis of a biopolyol from a wood residue by means of a scaled-up process with suitable yield and reaction conditions was carried out. This biopolyol was able to substitute completely the synthetic polyols that are typically employed within a polyurethane formulation. Different formulations were developed to assess the effect of two flame retardants, namely, polyhedral oligomeric silsesquioxane (POSS) and amino polyphosphate (APP), in terms of their thermal properties and degradation and their fireproofing mechanism. The structure and the thermal degradation of the different formulations was evaluated via Fourier Transformed Infrared Spectroscopy (FTIR) and thermogravimetric analysis (TGA). Likewise, the performance of the different PUF formulations was studied and compared to that of an industrial PUF. From these results, it can be highlighted that the addition of the flame retardants into the formulation showed an improvement in the results of the UL-94 vertical burning test and the LOI. Moreover, the fireproofing performance of the biobased formulations was comparable to that of the industrial one. In addition to that, it can be remarked that the biobased formulations displayed an excellent performance as thermal insulators (0.02371–0.02149 W·m−1·K−1), which was even slightly higher than that of the industrial one.