We employ molecular dynamics simulations to explore the effect of tensile strain on the thermal conductivity of carbon nanotube (CNT)–graphene junction structures. Two types of CNT–graphene junctions are simulated; a seamless junction between CNT and graphene with pure sp2sp2 covalent bonds, and a junction with mixed sp2∕sp3sp2∕sp3 covalent bonds are studied. The most interesting observation is that the thermal conductivity of a CNT–graphene junction structure increases with an increase in mechanical strain. For the case of a (6,6) CNT–graphene junction structure with an inter-pillar distance (the length of graphene floor between two CNT–graphene junctions) of 15nm, the thermal conductivity is improved by 22.4% with 0.1 tensile strain. The thermal conductivity improvement by mechanical strain is enhanced when a larger graphene floor is placed between junctions since a larger graphene floor allows larger deformation (larger tensile strain) without breaking bonds in the junction structure. However, the thermal conductivity is found to more strongly depend on the C–C bond hybridization at the intramolecular junctions with pure sp2sp2 hybridization showing a higher thermal conductivity when compared to mixed sp2∕sp3sp2∕sp3 bonding regardless of the amount of tensile strain. The obtained results will contribute to the development of flexible electronics by providing a theoretical background on the thermal transport of three-dimensional carbon nanostructures under deformation.