  The ability to probe nanoscale heat flow in a material is often limited by
lack of spatial resolution. Here, we use a diamond-nanocrystal-hosted
nitrogen-vacancy centre attached to the apex of a silicon thermal tip as a
local temperature sensor. We apply an electrical current to heat up the tip and
rely on the NV to monitor the thermal changes the tip experiences as it is
brought into contact with surfaces of varying thermal conductivity. With the
aid of a combined AFM/confocal setup, we image phantom microstructures with
nanoscale resolution, and attain excellent agreement between the thermal
conductivity and topographic maps. The small mass and high thermal conductivity
of the diamond host make the time response of our technique short, which we
demonstrate by monitoring the tip temperature upon application of a heat pulse.
Our approach promises multiple applications, from the investigation of phonon
dynamics in nanostructures to the characterization of heterogeneous phase
transitions and chemical reactions in various solid-state systems.
