Carbon nanotubes are emerging as a possible new candidate material for thermal management applications, owing to their high reported intrinsic thermal conductivity, when measured as individual nanostructures. However, studies on bulk samples of nanotubes, solutions, and composites all show relatively low thermal conductivity. This is believed to be due to high interfacial thermal resistance. I will present novel studies, in situ during transmission electron microscopy, that allow thermal propoerties of individual nanotubes to be interrogated. These studies show high interfacial thermal resistance, but also a surprising ability for nanotubes to transfer heat to a substrate when carrying a DC electrical current. This will be explained in terms of a new physical phenomenon, a new mechanism of heating, that we have called remote Joule heating, and I will make connections with theories predicting the effect.