Electron-beam-induced deposition (EBID) of carbon on the surface of carbon nanotubes was well controlled by passing different electrical currents through the nanotubes. The control is due to Joule heating and the temperature of the carbon nanotubes was estimated. The deposition rate was found to increase and then decrease with the temperature and was maximized at about 310 K and approached zero at about 400 K. The method can be used to control the deposition rate of EBID in nanowelding and nanofabrication and to eliminate amorphous carbon contamination in in situ study of nanostructures.