  Temperature imaging of nanoscale systems is a fundamental problem which has
myriad potential technological applications. For example, nanoscopic cold spots
can be used for spot cooling electronic components while hot spots could be
used for precise activation of chemical or biological reactions. More
fundamentally, imaging the temperature fields in quantum coherent conductors
can provide a wealth of information on heat flow and dissipation at the
smallest scales. However, despite significant technological advances, the
spatial resolution of temperature imaging remains in the few nanometers range.
Here we propose a method to map electronic temperature variations in operating
nanoscale conductors by relying solely upon electrical tunneling current
measurements. The scanning tunneling thermometer, owing to its operation in the
tunneling regime, would be capable of mapping sub-angstrom temperature
variations, thereby enhancing the resolution of scanning thermometry by some
two orders of magnitude.
