Low-quality waste oils and fats such as the oily content of trap grease offer an alternative to fossil fuel oil, but they are not fully utilized since they contain saturated fatty acids (SFAs) and saturated triglycerides (STGs), which have relatively high melting points. For practical use of the oily content, it is necessary to remove the components that are solid at room temperature. In this study, we measured the liquidus curves of systems comprising an SFA (stearic acid, palmitic acid, or myristic acid) or an STG (tristearin, tripalmitin, or trimyristin) plus fuel oil A by differential scanning calorimetry. At the same mass fraction of the solid component, the STG plus fuel oil A systems had higher liquidus temperatures than the SFA plus fuel oil A systems with the same fatty acid chains. In both of the SFA plus fuel oil A systems and the STG plus fuel oil A systems, the system in which the solid component had a longer carbon chain had a higher liquidus temperature. On the assumption that fuel oil A is a pseudo-pure component, we proposed two simple methods for predicting liquidus temperature, from the ideal solution approximation and the Dortmund-UNIFAC model, and evaluated their prediction performance by comparing the experimental liquidus curves and the calculated results.