In this research, the thermal transport behavior of the branched carbon nanotube (CNT) with T-junction was investigated using non-equilibrium molecular dynamics simulation. Both symmetric and asymmetric temperature-controlled simulations were imposed to evaluate how the heat flowed inside the branched CNT with three branches of equal length and same chirality. The branch length and strain effects on the heat flow were examined. In addition, the simulated heat flow was compared with the prediction made by conventional thermal circuit calculation based on diffusive phonon transport. The heat was observed to flow straight rather than sideway inside the branched CNT with T-junction under the asymmetric temperature setup; this finding contradicts the conventional thermal circuit calculation. There are two possible explanations for this phenomenon. One is ballistic phonon transport and the other is phonons have different interactions or scattering with the defective atomic configurations at the T-junction. Moreover, the tensile strain could tune the heat flow, a finding that might be useful in thermal management applications.