This article deals with the study of the viscoelastic and thermal properties of polyurethane (PU) rigid foams from biobased and recycled components. Rapeseed oil (RO) and recycled poly(ethylene terephthalate) (PET) were used to synthesize PU polyols. Addition of adipic acid (ADA) to polyol resulted in improved thermal and viscoelastic properties of foam materials. ADA content was varied from 1 to 6 wt%. Results of the dynamic mechanical spectra indicate an increase of the storage modulus E′ and the loss modulus E″ in the whole temperature range for specimens with higher loading of ADA. In addition, damping factor shifted to higher temperatures, but damping intensity remained almost unaffected by the compositions. Scanning electron microscopy of the foams’ cross sections testified that the average cells’ size of 110 mm was unaffected by the ADA content in polyol.