Data uncertainty is commonly observed in the images for face recognition (FR). However, deep learning algorithms often make predictions with high confidence even for uncertain or irrelevant inputs. Intuitively, FR algorithms can benefit from both the estimation of uncertainty and the detection of out-of-distribution (OOD) samples. Taking a probabilistic view of the current classification model, the temperature scalar is exactly the scale of uncertainty noise implicitly added in the softmax function. Meanwhile, the uncertainty of images in a dataset should follow a prior distribution. Based on the observation, a unified framework for uncertainty modeling and FR, Random Temperature Scaling (RTS), is proposed to learn a reliable FR algorithm. The benefits of RTS are two-fold. (1) In the training phase, it can adjust the learning strength of clean and noisy samples for stability and accuracy. (2) In the test phase, it can provide a score of confidence to detect uncertain, low-quality and even OOD samples, without training on extra labels. Extensive experiments on FR benchmarks demonstrate that the magnitude of variance in RTS, which serves as an OOD detection metric, is closely related to the uncertainty of the input image. RTS can achieve top performance on both the FR and OOD detection tasks. Moreover, the model trained with RTS can perform robustly on datasets with noise. The proposed module is light-weight and only adds negligible computation cost to the model.