Palm or coconut oil is capable of dissolving in a mixture of bisphenol A-based epoxy resin and a high-temperature hardener (4,4′-diaminodiphenyl sulfone) when heated and then forms a dispersed phase as a result of cross-linking and molecular weight growth of the epoxy medium. Achieving the temporary miscibility between the curing epoxy matrix and the vegetable oil allows a uniform distribution of vegetable oil droplets in the epoxy medium. This novel approach to creating a dispersed phase-change material made a cured epoxy polymer containing up to 20% oil. The miscibility of epoxy resin and oil was studied by laser interferometry, and phase state diagrams of binary mixtures were calculated according to theory and experiments. A weak effect of oil on the viscosity and kinetics of the epoxy resin curing was demonstrated by rotational rheometry. According to differential scanning calorimetry and dynamic mechanical analysis, the oil plasticizes the epoxy matrix slightly, expanding its glass transition region towards low temperatures and reducing its elastic modulus. In the cured epoxy matrix, oil droplets have a diameter of 3–14 µm and are incapable of complete crystallization due to their multi-component chemical composition and non-disappeared limited miscibility. The obtained phase-change materials have relatively low specific energy capacity but can be used alternatively as self-lubricating low-noise materials due to dispersed oil, high stiffness, and reduced friction coefficient. Palm oil crystallizes more readily, better matching the creation of phase-change materials, whereas coconut oil crystallization is more suppressed, making it better for reducing the friction coefficient of the oil-containing material.