Fusion of parallel finite length single-walled carbon nanotubes (SWCNTs) without initially introducing structural defects is investigated by molecular dynamics (MD) simulations. Three different models that impose different constraints are adopted to simulate the heat welding and coalescence of the parallel SWCNTs. It is found that the ultrathin as well as some larger diameter, finite length SWCNTs, for example (8,0) and (10,0) SWCNTs can be coalesced to become a unique single-walled tube solely via high temperature heat treatment. It is observed that the ends of the nanotubes are prone to close at high temperature during the high temperature treatment. In addition, the fusion process and mechanism of parallel SWCNTs with different lengths and radii are discussed.