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This article investigates the effects of two types of nanoparticles, OctaMethylOligomericSilsesquioxanes (OMPOSS) and carbon nanotubes (CNTs), in a model epoxy resin. Intumescent phosphorous-based flame-retardant (APP) was also incorporated with the CNTs. Thermal conductivity of nanocomposites was measured using a thermal analyser with the transient plane source method. Epoxy with APP and OMPOSS had increasing thermal conductivity below the glass transition temperature (Tg) but slowed above Tg. When APP and CNTs were combined, CNTs hid the effects of APP, leading to a decrease in thermal conductivity.