Graphene is an outstanding material with ultrahigh thermal conductivity.Its thermal transfer properties under various strains are studied by reverse nonequilibrium molecular dynamics.Based on the unique two-dimensional structure of graphene, the distinctive geometries of graphene sheets and graphene nanoribbons with large flexibility and their intriguing thermal properties are demonstrated under strains.For example, the corrugation under uniaxial compression and helical structure under light torsion, as well as tube-like structure under strong torsion, exhibit enormously different thermal conductivity.