Carbon nanotubes used as conductive atomic force microscopy probes are expected to withstand extremely high currents. However, in existing prototypes, significant self-heating results in rapid degradation of the nanotube probe. Here, we investigate an alternative probe design, fabricated by dielectric encapsulation of multiwalled carbon nanotubes, which can support unexpectedly high currents with extreme stability. We show that the dielectric coating acts as a reservoir for Joule heat removal, and as a chemical barrier against thermal oxidation, greatly enhancing transport properties. In contact with Au surfaces, these probes can carry currents of 0.12 mA at a power of 1.5 mW and show no measurable change in resistance at current densities of 10(12) A/m(2) over a time scale of 10(3) s. Our observations are in good agreement with theoretical modeling and exact numerical calculations, demonstrating that the enhanced transport characteristics of such probes are governed by their more effective heat removal mechanisms.