Abstract The nanoscale thermal conductivity of a material can be significantly different from its value at the macroscale. Although a number of studies using the equilibrium molecular dynamics (EMD) with Green–Kubo (GK) formula have been conducted for nano-conductivity predictions, there are many problems in the analysis that have made the EMD results unreliable or misleading. This paper aims to clarify such critical issues through a thorough investigation on the effect and determination of the vital physical variables in the EMD-GK analysis, using the prediction of the nanoscale thermal conductivity of Si as an example. The study concluded that to have a reliable prediction, quantum correction, time step, simulation time, correlation time and system size are all crucial.