Negative refractive index has drawn a great deal of attention due to its unique properties and practical applications in wave systems.To promote the related physics in thermotics,here we manage to coin a complex thermal conductivity whose imaginary part corresponds to the real part of complex refractive index.Therefore,the thermal counterpart of negative refractive index is just negative imaginary thermal conductivity,which is featured by the opposite directions of energy flow and wave vector in thermal conduction and advection,thus called negative thermal transport herein.To avoid violating causality,we design an open system with energy exchange and explore three different cases to reveal negative thermal transport.We further provide experimental suggestions with a solid ring structure.All finite-element simulations agree with theoretical analyses,indicating that negative thermal transport is physically feasible.These results have potential applications such as designing the inverse Doppler effect in thermal conduction and advection.