Measuring temperature is a central challenge in nanoscience and technology. Addressing this challenge, we report the development of a high-vacuum scanning thermal microscope and a method for non-equilibrium scanning probe thermometry. The microscope is built inside an electromagnetically shielded, temperature-stabilized laboratory and features nanoscopic spatial resolution at sub-nanoWatt heat flux sensitivity. The method is a dual signal-sensing technique inferring temperature by probing a total steady-state heat flux simultaneously to a temporally modulated heat flux signal between a self-heated scanning probe sensor and a sample. Contact-related artifacts, which so far limit the reliability of nanoscopic temperature measurements by scanning thermal microscopy, are minimized. We characterize the microscope's performance and demonstrate the benefits of the new thermometry approach by studying hot spots near lithographically defined constrictions in a self-heated metal interconnect.