This work, for the first time, experimentally demonstrates a TCAD-Machine Learning (TCAD-ML) framework to assist the analysis of device-to-device variation and operating (ambient) temperature without the need of physical quantities extraction. The ML algorithm used in this work is the Principal Component Analysis (PCA) followed by third order polynomial regression. After calibrated to limited 'expensive' experimental data, 'low cost' TCAD simulation is used to generate a large amount of device data to train the ML model. The ML was then used to identify the root cause of device variation and operating temperature from any given experimental current-voltage (I-V) characteristics. We applied this framework to study the ultra-wide-bandgap gallium oxide (Ga2O3) Schottky barrier diode (SBD), an emerging device technology that holds great promise for temperature sensing, RF, and power applications in harsh environments. After calibration, over 150,000 electrothermal TCAD simulations are performed with random variation of physical parameters (anode effective work function, drift layer doping, and drift layer thickness) and operating temperature. An ML model is trained using these TCAD data and we found 1,000-10,000 TCAD data can train an accurate machine. We show that without physical quantities extraction, performing PCA is essential for the TCAD trained ML model to be applicable to analyze experimental characteristics. The physical parameters and temperatures predicted by the ML model show good agreement with experimental analysis. Our TCAD-ML framework shows great promise to accelerate the development of new device technologies with a significantly more efficient process of material and device experimentation.