A fully-automatic approach based on the use of induction thermography and detection algorithms is proposed to inspect industrial metallic parts containing different surface and sub-surface anomalies such as open cracks, open and closed notches with different sizes and depths. A practical experimental setup is developed, where lock-in and pulsed thermography (LT and PT, respectively) techniques are used to establish a dataset of thermal images for three different mockups. Data cubes are constructed by stacking up the temporal sequence of thermogram images. After the reduction of the data space dimension by means of denoising and dimensionality reduction methods; anomaly detection algorithms are applied on the reduced data cubes. The dimensions of the reduced data spaces are automatically calculated with arbitrary criterion. The results show that, when reduced data cubes are used, the anomaly detection algorithms originally developed for hyperspectral data, that of Reed and Xiaoli Yu (RX) and the regularized adaptive RX (RARX), give good detection performances for both surface and sub-surface defects in a non-supervised way.