In Automatic Speech Recognition (ASR) systems, a recurring obstacle is the generation of narrowly focused output distributions. This phenomenon emerges as a side effect of Connectionist Temporal Classification (CTC), a robust sequence learning tool that utilizes dynamic programming for sequence mapping. While earlier efforts have tried to combine the CTC loss with an entropy maximization regularization term to mitigate this issue, they employed a constant weighting term on the regularization during the training, which we find may not be optimal. In this work, we introduce Adaptive Maximum Entropy Regularization (AdaMER), a technique that can modulate the impact of entropy regularization throughout the training process. This approach not only refines ASR model training but ensures that as training proceeds, predictions display the desired model confidence.