This work investigates the molecular interactions within the main triacylglycerols constitutive of palm oil, all having a key role in the multi-step dry fractionation process. Identification of these interactions is possible thanks to the establishment of binary and ternary phase diagrams, using differential scanning calorimetry (DSC) and powder X-ray diffraction (XRD) at variable temperature. The following systems were selected: PPP-POP, PPP-OPP, PPP-POO, POP-OPP, POP-POO, OPP-POO, PPP-POP-POO and PPP-OPP-POO (P: palmitic acid and O: oleic acid), and analyzed in direct mode (heating at 5 °C/min., after melting and quenching at −60 °C), and after tempering for three months at 20 °C (tempered mode). DSC makes it possible to bring out crystallization and melting phenomena associated to polymorphic transitions, which are further characterized (crystalline forms) by XRD. The results show that unsaturated are poorly soluble in fully saturated triacylglycerols, that the intersolubility decreases in proportion to the number of unsaturated fatty acids, that positional isomerism (POP/OPP) has a major impact, that OPP may induce formation of molecular compounds and that co-crystallization properties are highly modified by tempering depending on the polymorphic properties of the systems. This provides a better understanding and allows for effective control of the palm oil dry fractionation process.