As per Wikipedia
While there have been reports of intrinsic superconductivity in carbon nanotubes, many other experiments found no evidence of superconductivity, and the validity of these results remains a subject of debate.
From Sciecemag
Investigation of the magnetic and transport properties of single-walled small-diameter carbon nanotubes embedded in a zeolite matrix revealed that at temperatures below 20 kelvin, 4 angstrom tubes exhibit superconducting behavior manifest as an anisotropic Meissner effect, with a superconducting gap and fluctuation supercurrent. The measured superconducting characteristics display smooth temperature variations owing to one-dimensional fluctuations, with a mean-field superconducting transition temperature of 15 kelvin.
From New Scientist
Tiny tubes of carbon may conduct electricity without any resistance, at temperatures stretching up past the boiling point of water. The tubes would be the first superconductors to work at room temperature.
Each nanotube is typically a millionth of a metre long, several billionths of a metre in diameter and with walls a few atoms thick. The nanotubes cling together in oblong bundles about a millimetre in length.
The researchers did not see zero resistance in their bundles. They think this is because the connections between the tiny tubes never become superconducting. But they did see more subtle signs of superconductivity within the tubes themselves.
For example, when the researchers put a magnetic field across a bundle at temperatures up to 400 kelvin ($127°\mathrm{C}$), the bundle generated its own weak, opposing magnetic field. Such a reaction can be a sign of superconductivity.