Deep learning systems often struggle with processing long sequences, where computational complexity can become a bottleneck. Current methods for automated dementia detection using speech frequently rely on static, time-agnostic features or aggregated linguistic content, lacking the flexibility to model the subtle, progressive deterioration inherent in speech production. These approaches often miss the dynamic temporal patterns that are critical early indicators of cognitive decline. In this paper, we introduce TAI-Speech, a Temporal Aware Iterative framework that dynamically models spontaneous speech for dementia detection. The flexibility of our method is demonstrated through two key innovations: 1) Optical Flow-inspired Iterative Refinement: By treating spectrograms as sequential frames, this component uses a convolutional GRU to capture the fine-grained, frame-to-frame evolution of acoustic features. 2) Cross-Attention Based Prosodic Alignment: This component dynamically aligns spectral features with prosodic patterns, such as pitch and pauses, to create a richer representation of speech production deficits linked to functional decline (IADL). TAI-Speech adaptively models the temporal evolution of each utterance, enhancing the detection of cognitive markers. Experimental results on the DementiaBank dataset show that TAI-Speech achieves a strong AUC of 0.839 and 80.6\% accuracy, outperforming text-based baselines without relying on ASR. Our work provides a more flexible and robust solution for automated cognitive assessment, operating directly on the dynamics of raw audio.