High-performance top-gate carbon nanotube (CNT) field-effect transistors (FETs) have been fabricated via a doping-free fabrication process in which the polarity of the CNT FET is controlled by the injection of carriers from the electrodes, instead of using dopants. The performance of the doping-free CNT FETs is systemically investigated over a wide temperature range, from very low temperatures of down to 4.3 K up to 573 K, and analyzed using several temperature-dependent key device parameters including the ON/OFF state current and ratio, carrier mobility, and subthreshold swing. It is demonstrated that for ballistic and quasi-ballistic CNT FETs, the operation of the CNT FETs is largely independent of the presence of dopant, thus avoiding detrimental effects due to dopant freeze-out at low temperature and dopant diffusion at high temperature, and making it possible to use doping-free CNT FETs in both low-and high-temperature electronics. A new method is also proposed for extracting the band-gap and diameter of a semiconducting CNT from the temperature dependent OFF-state current and shown to yield results that are consistent with AFM measurements.