  Scanning Thermal Microscopy (SThM) has become an important measurement tool
for characterizing the thermal properties of materials at the nanometer scale.
This technique requires a SThM probe that combines an Atomic Force Microscopy
(AFM) probe and a very sensitive resistive thermometry; the thermometer being
located at the apex of the probe tip allows the mapping of temperature or
thermal properties of nanostructured materials with very high spatial
resolution. The high interest of the SThM technique in the field of thermal
nanoscience currently suffers from a low temperature sensitivity despite its
high spatial resolution. To address this challenge, we developed a high
vacuum-based AFM system hosting a highly sensitive niobium nitride (NbN) SThM
probe to demonstrate its unique performance. As a proof of concept, we utilized
this custom-built system to carry out thermal measurements using the 3$\omega$
method. By measuring the $V_{3\omega}$ voltage on the NbN resistive thermometer
in vacuum conditions we were able to determine the SThM probe's thermal
conductance and thermal time constant. The performance of the probe is
demonstrated by doing thermal measurements in-contact with a sapphire sample.
