In this study, the influence of the degree of unsaturation of the triglyceride on the composition of the products of the thermal cracking process, in particular the formation of aromatic compounds, was investigated. Experiments were performed using triglyceride sources with different degrees of unsaturation, maintaining the same operational conditions. Analysis of the products revealed that a greater amount of aromatic compounds is formed during the thermal cracking of biomass with a higher degree of unsaturation. The aromatics content in the liquid product decreased by 14% in the cracking of biomass with the lowest unsaturated content. A correlation between the aromatics content and the iodine index of the sample was proposed, as a simple way to estimate the aromatics content in bio-oil. It was also observed that the reactions for carboxyl removal were favorable in the case of saturated compounds, the acidity index reducing from 210.9 to 139.0 gKOH/g in the biomass with the lowest unsaturated content. However, long-chain paraffinic compounds were present in the products, which suggests that a catalyst or more severe conditions might be necessary for the biomass cracking.