Developing polyols derived from natural sources and recycling materials attracts great interest for use in replacing petroleum-based polyols in polyurethane production. In this study, rigid polyurethane (PUR) foams with various isocyanate indices were obtained from polyols based on rapeseed oil and polyethylene terephthalate (RO/PET). The various properties of the prepared PUR foams were investigated, and the effect of the isocyanate index was evaluated. The closed-cell content and water absorption were not impacted by the change of the isocyanate index. The most significant effect of increasing the isocyanate index was on the dimensional stability of the resulting foams. This is due to the increased crosslink density, as evidenced by the increased formation of isocyanurate and increase of the glass transition temperature. Additionally, the influence on compression strength, modulus, and long-term thermal conductivity were evaluated and compared with reference PUR foams from commercially available polyols. Rigid PUR foams from RO/PET polyol were found to be competitive with reference materials and could be used as thermal insulation material.