Devices with a highly nonlinear resistance-voltage relationship are candidates for neuromorphic computing, which can be achieved by highly temperature dependent processes like ion migration. To explore the thermal properties of such devices, Scanning Thermal Microscopy (SThM) can be employed. However, due to the nonlinearity, the high resolution and quantitative method of AC-modulated SThM cannot readily be used. To this end, an extended nonequilibrium scheme for temperature measurement using SThM is proposed, with which the self-heating of nonlinear devices is studied without the need for calibrating the tip-sample contact for a specific material combination, geometry or roughness. Both a DC and an AC voltage are applied to the device, triggering a periodic temperature rise, which enables the simultaneous calculation of the tip-sample thermal resistance and the device temperature rise. The method is applied to HfO