A straightforward and sensitive approach is presented for contact-free thermal sensing with high spatial resolution based on optically detected magnetic resonance (ODMR) of negatively charged nitrogen-vacancy (NV) centers in fluorescent nanodiamonds. The frequency-jump procedure is a frequency modulation technique between two discrete frequencies at the inflection points at both sides of the NV ODMR resonance, which yields a signal proportional to the temperature shift over a wide temperature range. The approach is generic and is demonstrated by time-dependent measurements of the local temperature at different spots on a microelectronics circuit under electrical switching operation of one of the devices.