The effects of thermal treatment on CNTs, which were coated with a-$CN_x$ thin film, were investigated and related to variations of chemical bonding and morphologies of CNTs and also properties of field emission induced by thermal treatment. CNTs were directly grown on nano-sized conical-type tungsten tips via the inductively coupled plasma-chemical vapor deposition (ICP-CVD) system, and a-$CN_x$ films were coated on the CNTs using an RF magnetron sputtering system. Thermal treatment on a-$CN_x$ coated CNT-emitters was performed using a rapid thermal annealing (RTA) system by varying temperature ($300-700^{circ}C$). Morphologies and microstructures of a-$CN_x$/CNTs hetero-structured emitters were analyzed by FESEM and HRTEM. Chemical composition and atomic bonding structures were analyzed by EDX, Raman spectroscopy, and XPS. The field emission properties of the a-$CN_x$/CNTs hetero-structured emitters were measured using a high vacuum (below $10^{-7}$ Torr) field-emission measurement system. For characterization of emission stability, the fluctuation and degradation of the emission current were monitored in terms of operation time. The results were compared with a-$CN_x$ coated CNT-emitters that were not thermally heated as well as with the conventional non-coated CNT-emitters.