High-entropy alloys (HEAs) are alloys composed of five or more primary elements in equal or nearly equal proportions of atoms. HEAs have excellent mechanical properties for a wide temperature range and have been applied to a wide range of areas. The underlying mechanism for heat transfer in HEAs is unclear and relevant studies are still lacking. In the present study, a molecular dynamics method is adopted to explore the lattice thermal conductivity of the equiatomic CoCrFeNiCu high entropy alloy at the nanoscale. The effects of alloy size and temperature on the lattice thermal conductivity of equiatomic CoCrFeNiCu are investigated. Results indicate that lattice thermal conductivity increases with alloy size. The lattice thermal conductivity decreases as the temperature increases, and a mathematical relationship between the lattice thermal conductivity and temperature is provided. To reveal the mechanism for the effect of temperature on the lattice thermal conductivity, the phonon density of states is calculated. The preliminary results presented in this study demonstrate the molecular dynamics method is a powerful tool to reveal the microscale mechanism for heat transfer in HEAs. This study provides theoretical foundations for high-resolution thermal design and has implications for high-performance alloy smelting. In future research, additional thermophysical properties, like heat capacity, of HEAs will be explored.