Initially, three samples of carbon nanotubes (SWCNTs) were synthesized from neem tree material. Afterward, these samples were coated with hexagonal boron nitride (h-BN) to form h-BN and CNT composite (h-BN-CNT). The essence of using h-BN (being a perfect insulator) with armchair SWCNT (being a conductor) is to create an interface between an insulator and conductor. The samples were treated under three different transition metal nanoparticles; silver, iron, and nickel. Thermogravimetric (TGA) analysis reveals that h-BN/CNT is thermally more stable with silver than iron and nickel nanoparticles. TGA profile showed resistance to mass loss at the beginning due to the higher thermal resistivity by the impurity compounds. The DFT calculation, generalized gradient approximation (GGA), and Perdew–Burke–Ernzerhof (PBE) analysis found engineered bandgap energy of 3.4 eV for the synthesized h-BN-CNT heterostructure. Because of its unique structural and electronic properties such as tunable bandgaps, the h-BN-CNT heterostructure may open new ways for manipulating excitons in the CNTs, and thus can be explored to develop various new electronic devices.