Scanning Thermal Microscopy (SThM) uses micromachined thermal sensors integrated in a force sensing cantilever with a nanoscale tip can be highly useful for exploration of thermal management of nanoscale semiconductor devices. As well as mapping of surface properties of related materials. Whereas SThM is capable to image externally generated heat with nanoscale resolution, its ability to map and measure thermal conductivity of materials has been mainly limited to polymers or similar materials possessing low thermal conductivity in the range from 0.1 to 1 W/mK, with lateral resolution on the order of 1 \mum. In this paper we use linked experimental and theoretical approaches to analyse thermal performance and sensitivity of the micromachined SThM probes in order to expand their applicability to a broader range of nanostructures from polymers to semiconductors and metals. We develop physical models of interlinked thermal and electrical phenomena in these probes and then validate these models using experimental measurements of the real probes, which provided the basis for analysing SThM performance in exploration of nanostructures. Our study then highlights critical features of these probes, namely, the geometrical location of the thermal sensor with respect to the probe apex, thermal conductance of the probe to the support base, heat conduction to the surrounding gas, and the thermal conductivity of tip material adjacent to the apex. It is furthermore allows us to propose a novel design of the SThM probe that incorporates a carbon nanotube (CNT) or similar high thermal conductivity graphene sheet material positioned near the probe apex. The new sensor is predicted to provide spatial resolution to the thermal properties of nanostructures on the order of few tens of nm, as well as to expand the sensitivity of the SThM probe to materials with heat conductivity values up to 100-1000 W/mK.