Classification models based on deep neural networks (DNNs) must be calibrated to measure the reliability of predictions. Some recent calibration methods have employed a probabilistic model on the probability simplex. However, these calibration methods cannot preserve the accuracy of pre-trained models, even those with a high classification accuracy. We propose an accuracy-preserving calibration method using the Concrete distribution as the probabilistic model on the probability simplex. We theoretically prove that a DNN model trained on cross-entropy loss has optimality as the parameter of the Concrete distribution. We also propose an efficient method that synthetically generates samples for training probabilistic models on the probability simplex. We demonstrate that the proposed method can outperform previous methods in accuracy-preserving calibration tasks using benchmarks. The code is available at https://github.com/ToyotaCRDL/SimplexTS.