Isolated individual carbon nanotubes (CNTs) have shown exceptional thermal conductivity along their axis, but have poor thermal transfer between adjacent CNTs. Thick bundles of aligned CNTs have been used as heat pipes, but the thermal input and output areas are the same, providing no heat spreading effect. We demonstrate the use of energetic argon ion beams to join overlapping CNTs in a thin film to form an interpenetrating network with an isotropic thermal conductivity of 2150 W/m-K. Such thin films may be used as heat spreaders to enlarge the thermal footprint of laser diodes and CPU chips, for example, for enhanced cooling. At higher ion energies and fluence, the CNTs appear to collapse and reform, aligned parallel to the ion beam axis, and form dense high aspect ratio tapered structures. The high surface area of these structures lends themselves to applications in energy storage, for example. We consider the mechanisms of energetic ion interaction with CNTs and junction formation of two overlapping CNTs during the subsequent self-healing process, as well as the formation of high aspect ratio structures under more extreme conditions.