We report on a thermal imaging technique based on fluorescence polarization anisotropy measurements, which enables mapping the local temperature near nanometer-sized heat sources with 300 nm spatial resolution and a typical accuracy of 0.1 degrees C. The principle is demonstrated by mapping the temperature landscape around plasmonic nano-structures heated by near-infrared light. By assessing directly the molecules' Brownian dynamics, it is shown that fluorescence polarization anisotropy is a robust and reliable method which overcomes the limitations of previous thermal imaging techniques. It opens new perspectives in medicine, nanoelectronics and nanofluidics where a control of temperature of a few degrees at the nanoscale is required.