A second-generation bio-based feedstock—tall oil fatty acids—was epoxidised via two pathways. Oxirane rings were introduced into the fatty acid carbon backbone using a heterogeneous epoxidation catalyst-ion exchange resin Amberlite IR-120 H or enzyme catalyst Candida antarctica lipase B under the trade name Novozym® 435. High functionality bio-polyols were synthesised from the obtained epoxidated tall oil fatty acids by oxirane ring-opening and subsequent esterification reactions with different polyfunctional alcohols: trimethylolpropane and triethanolamine. The synthesised epoxidised tall oil fatty acids (ETOFA) were studied by proton nuclear magnetic resonance. The chemical structure of obtained polyols was studied by Fourier-transform infrared spectroscopy and size exclusion chromatography. Average molecular weight and polydispersity of polyols were determined from size exclusion chromatography data. The obtained polyols were used to develop rigid polyurethane (PU) foam thermal insulation material with an approximate density of 40 kg/m3. Thermal conductivity, apparent density and compression strength of the rigid PU foams were determined. The rigid PU foams obtained from polyols synthesised using Novozym® 435 catalyst had superior properties in comparison to rigid PU foams obtained from polyols synthesised using Amberlite IR-120 H. The developed rigid PU foams had an excellent thermal conductivity of 21.2–25.9 mW/(m·K).