Composite phase-change materials (PCMs), consisting of nanoparticle metal or metal oxide suspended in an organic PCM, are considered promising for overcoming the significant drawbacks of organic PCM, particularly their relatively low thermal conductivity. This paper presents an experimental study of the performance of composite PCMs in terms of chemical stability, thermal stability, phase transition temperature, latent heat, thermal conductivity, and viscosity related to freezing characteristics. The composite PCM consists of an organic PCM of lauric acid (LA) and magnetic dopants of Fe3O4 and CoFe2O4 at concentrations of 2, 5, and 10 wt%. The freezing data revealed the time and temperature characteristics related to the beginning of freezing, the end of the solidification process, and the total crystallisation period. For dopant concentrations below 5 wt%, the dopant increased the heat transfer rate and accelerated the solidification process. However, its effectiveness at the highest dopant concentration of 10 wt% was highly dependent on the microstructure of the dopant particles and its effect on viscosity and thermal conductivity. Based on the data analysis, we proposed a maximum dopant concentration of 5 wt% for the optimum performance of the composite LA using a magnetic dopant—dependent on the particle size that determined the interparticle magnetic dipolar interaction. However, compared with previous experimental findings for non-magnetic dopant particles, the composite FA using a magnetic dopant showed a lower thermal conductivity enhancement and lower time savings for solidification.