Test-Time Adaptation (TTA) is a critical paradigm for tackling distribution shifts during inference, especially in visual recognition tasks. However, while acoustic models face similar challenges due to distribution shifts in test-time speech, TTA techniques specifically designed for acoustic modeling in the context of open-world data shifts remain scarce. This gap is further exacerbated when considering the unique characteristics of acoustic foundation models: 1) they are primarily built on transformer architectures with layer normalization and 2) they deal with test-time speech data of varying lengths in a non-stationary manner. These aspects make the direct application of vision-focused TTA methods, which are mostly reliant on batch normalization and assume independent samples, infeasible. In this paper, we delve into TTA for pre-trained acoustic models facing open-world data shifts. We find that noisy, high-entropy speech frames, often non-silent, carry key semantic content. Traditional TTA methods might inadvertently filter out this information using potentially flawed heuristics. In response, we introduce a heuristic-free, learning-based adaptation enriched by confidence enhancement. Noting that speech signals' short-term consistency, we also apply consistency regularization during test-time optimization. Our experiments on synthetic and real-world datasets affirm our method's superiority over existing baselines.