The　numerical　manifold　method　(NMM)　introduces　the　mathematical　and　physical　cover　to　solve　both　continuum　and　discontinuum　problems　in　a　unified　manner.　In　this　study,　the　NMM　for　solving　steady-state　nonlinear　heat　conduction　problems　is　presented,　and　heat　conduction　problems　consider　both　convection　and　radiation　boundary　conditions.　First,　the　nonlinear　governing　equation　of　thermal　conductivity,　which　is　dependent　on　temperature,　is　transformed　into　the　Laplace　equation　by　introducing　the　Kirchhoff　transformation.　The　transformation　reserves　linearity　of　both　the　Dirichlet　and　the　Neumann　boundary　conditions,　but　the　Robin　and　radiation　boundary　conditions　remain　nonlinear.　Second,　the　NMM　is　employed　to　solve　the　Laplace　equation　using　a　simple　iteration　procedure　because　the　nonlinearity　focuses　on　parts　of　the　problem　domain　boundaries.　Finally,　the　temperature　field　is　retrieved　through　the　inverse　Kirchhoff　transformation.　Typical　examples　are　analyzed,　demonstrating　the　advantages　of　the　Kirchhoff　transformation　over　the　direct　solution　of　nonlinear　equations　using　the　Newton-Raphson　method.　This　study　provides　a　new　method　for　calculating　nonlinear　heat　conduction.　©　2023,　Science　China　Press.