Due　to　the　use　of　dual　cover　systems,　i.e.,　the　mathematical　cover　and　the　physical　cover,　the　numerical　manifold　method　(NMM)　is　able　to　solve　physical　problems　with　boundary　inconsistent　meshes.　Meanwhile,　n-gons　(n＞4)　are　very　impressive,　due　to　their　greater　flexibility　in　discretization,　less　sensitivity　to　volumetric　and　shear　locking,　and　better　suitability　for　complex　microstructures　simulation.　In　this　paper,　the　NMM,　combined　with　Wachspress-type　hexagonal　elements,　is　developed　to　solve　2D　transient　heat　conduction　problems.　Based　on　the　governing　equations,　the　NMM　temperature　approximation　and　the　modified　variational　principle,　the　NMM　discrete　formulations　are　deduced.　The　solution　strategy　to　time-dependent　global　equations　and　the　spatial　integration　scheme　are　presented.　The　advantages　of　the　proposed　approach　in　both　discretization　and　accuracy　are　demonstrated　through　several　typical　examples　with　increasing　complexity.　The　extension　of　polygonal　elements　in　unsteady　thermal　analysis　within　the　NMM　is　realized.　(C)　2017　Elsevier　Inc.　All　rights　reserved.