Field emission (FE) electron spectroscopy from an individual multiwalled carbon nanotube (MWNT) is used to measure quantitatively stable temperatures at the apex, T(A), of up to 2000 K induced by FE currents approximately 1 microA. The high T(A) is due to Joule heating along the length of the MWNT. These measurements also give directly the resistance of the individual MWNT which is shown to decrease with temperature, and explain the phenomenon of FE-induced light emission which was observed simultaneously. The heating permits thermal desorption of the MWNT and, hence, excellent current stability.