Molecular dynamics simulations have been used to investigate the nature of heat pulse propagation through a Y-junction carbon nanotube consisting of a (14,0) trunk splitting into a pair of (7,0) branches. For comparison, these simulations were also carried out on straight (7,0) and (14,0) carbon nanotubes. Simulations of the Y-junction nanotube were run in three different configurations: with the heat pulse originating in the trunk, in one of the branches, or in both of the branches simultaneously. All of the simulations were run at 0K, and the length of the pulse was 1ps. Results have shown that the heat pulse excites a variety of traveling phonon modes. It has been found that the junction impedes the propagation of these modes. Furthermore, it has been observed that traveling modes originating in the trunk pass through the junction more easily than those originating in the branches. This provides preliminary evidence for anisotropic heat flow in Y-junction nanotube structures at low temperatures. Finally, it is possible for a single phonon mode passing through the junction to generate multiple phonon modes on the other side, all with velocities less than or equal to the original mode.