A device and methods for use thereof in low-temperature thermal scanning microscopy, providing non-contact, non-invasive localized temperature and thermal conductivity measurements in nanometer scale ranges with a temperature resolution in the micro-Kelvin order. A superconductive cap mounted on the tip of an elongated support probe is electrically-connected to superconductive leads for carrying electrical current through the cap. The critical superconducting current of the leads is configured to be greater than the critical current supported by the cap, and the cap's critical current is configured to be a function of its temperature. Thus, the temperature of the cap is measured by measuring its critical superconducting current. In a related embodiment, driving a current greater than the critical current of the cap quenches the cap's superconductivity, and permits the cap to dissipate resistive heat into the sample being scanned. Scanning of the sample in this mode thus images its thermal conductivity patterns.