Real-time acquisition of accurate machine parameters is of significance to achieving high performance in electric drives, particularly targeted for mission-critical applications. Unlike the saturation effects, the temperature variations are difficult to predict, thus it is essential to track temperature-dependent parameters online. In this paper, a unified framework is developed for online parameter identification of rotating electric machines, premised on the Recursive Prediction Error Method (RPEM). Secondly, the prediction gradient (Psi(T))-based RPEM is adopted for identification of the temperature-sensitive parameters, i.e., the permanent magnet flux linkage (Psi(m)) and stator-winding resistance (R-s) of the Interior Permanent Magnet Synchronous Machine (IPMSM). Three algorithms, namely, Stochastic Gradient (SGA), Gauss-Newton (GNA), and physically interpretative method (PhyInt) are investigated for the estimation gains computation. A speed-dependent gain-scheduling scheme is used to decouple the inter-dependency of Psi(m) and Rs. With the aid of offline simulation methods, the main elements of RPEM such as Psi(T) are analyzed. The concept validation and the choice of the optimal algorithm is made with the use of System-on-Chip (SoC) based Embedded Real-Time Simulator (ERTS). Subsequently, the selected algorithms are validated with the aid of a 3-kW, IPMSM drive where the control and estimation routines are implemented in the SoC-based industrial embedded control system. The experimental results reveal that Psi(T) -based RPEM, in general, can be a versatile technique in temperature-sensitive parameter adaptation both online and offline.