Oxidative polymerization of plant oils and lipids is poorly understood yet widely encountered. Oils and fats are renewable resources providing biofuels and polymers. Oil oxidation is accelerated at high temperatures, typically above 110°C, where triacylglycerides are converted into toxic compounds and viscous deleterious polymers. Polymerization of mono‐unsaturated oil (210°C, 3 h, open to air) was investigated by comparing four similar sized molecules with different functional groups: oleic acid, methyl oleate, trans‐7‐tetradecene, and stearic acid. Non‐volatile products identified by NMR spectroscopy are minor ketones for saturated fatty acid (stearic acid), epoxides for acyl chains without acid groups (methyl oleate, tetradecane) and copious oligomerization, through ester cross‐links, for acyl chains with acid, and olefinic groups (oleic acid). Long range CH coupling clearly shows ester (not ether) cross‐links, contradicting long‐held beliefs. Chain fragmentation also occurs for heated oleic acid as revealed by formation of a species with a methylene group bonded to oxygen of an ester, CH2OC(O). Large size (slow diffusion) of the first oligomer (trimer) formed from oleic acid, used to represent hydrolyzed vegetable oil, was evidenced by DOSY (diffusion‐ordered spectroscopy). Combined NMR results show oligomers found in heated oleic acid are fatty acid estolides. Model oil reactions demonstrate why olefin and carboxylic acid groups are required for polymerization.