Polyunsaturated fatty acids (PUFA) are components in many commercial products such as edible oils, foods, cosmetics, medication and in biological systems such as phospholipids of cellular membranes. Though PUFA aggregates are important functional components, they are also related to system degradation, since PUFAs are susceptible to oxidation via their multiple double bonds and allylic carbons. Current technologies are not effective in characterizing the morphological and chemical structural domains of saturated, mono-unsaturated (MUFA) and PUFAs materials, or how the morphological structures of fatty acids, on the meso, nano and molecular levels, affect their oxidation mechanisms. In present study, the 1H Low Field (LF) NMR energy time relaxation sensorial technology is proposed as a tool to analyze PUFA-rich oils undergoing thermal oxidation. This technology generates 1D and 2D/3D chemical and morphological spectra using a primal dual interior method for the convex objectives optimization (PDCO) solver for computational processing of the energy relaxation time signals T1 (spin-lattice) and T2 (spin-spin). The 2D/3D graphical maps of T1 vs T2 generated for butter, rapeseed oil, soybean oil, linseed oil and pomegranate seed oil show that the different degrees of unsaturation of fatty acid oils affect their chemical and morphological domains, which influences their oxidative propensity. The technology of 1H LF-NMR energy relaxation time proved to be an effective non-destructive accurate and rapid sensorial tool to characterize and monitor PUFA oxidation.