Biometric technology is becoming increasingly prevalent in several vital applications that substitute traditional password and token authentication mechanisms. Recognition accuracy and computational cost are two important aspects that are to be considered while designing biometric authentication systems. Thermal imaging is proven to capture a unique thermal signature for a person and thus has been used in thermal face recognition. However, the literature did not thoroughly analyse the impact of feature selection on the accuracy and computational cost of face recognition which is an important aspect for limited resources applications like IoT ones. Also, the literature did not thoroughly evaluate the performance metrics of the proposed methods/solutions which are needed for the optimal configuration of the biometric authentication systems. This paper proposes a thermal face-based biometric authentication system. The proposed system comprises five phases: a) capturing the user’s face with a thermal camera, b) segmenting the face region and excluding the background by optimized superpixel-based segmentation technique to extract the region of interest (ROI) of the face, c) feature extraction using wavelet and curvelet transform, d) feature selection by employing bio-inspired optimization algorithms: grey wolf optimizer (GWO), particle swarm optimization (PSO) and genetic algorithm (GA), e) the classification (user identification) performed using classifiers: random forest (RF), k-nearest neighbour (KNN), and naive bayes (NB). Upon the public dataset, Terravic Facial IR, the proposed system was evaluated using the metrics: accuracy, precision, recall, F-measure, and receiver operating characteristic (ROC) area. The results showed that the curvelet features optimized using the GWO and classified with random forest could help in authenticating users through thermal images with performance up to 99.5% which is better than the results of wavelet features by 10% while the former used 5% fewer features. In addition, the statistical analysis showed the significance of our proposed model. Compared to the related works, our system showed to be a better thermal face authentication model with a minimum set of features, making it computational-friendly.