Generative conversational interfaces powered by large language models (LLMs) typically stream output token-by-token at a rate determined by computational budget, often neglecting actual human reading speeds and the cognitive load associated with the content. This mismatch frequently leads to inefficient use of computational resources. For example, in cloud-based services, streaming content faster than users can read appears unnecessary, resulting in wasted computational resources and potential delays for other users, particularly during peak usage periods. To address this issue, we propose an adaptive streaming method that dynamically adjusts the pacing of LLM streaming output in real-time based on inferred cognitive load. Our approach estimates the cognitive load associated with streaming content and strategically slows down the stream during complex or information-rich segments, thereby freeing computational resources for other users. We conducted a statistical analysis and simulation based on a statistical model derived from data collected in a crowdsourced user study across various types of LLM-generated content. Our results show that this adaptive method can effectively reduce computational consumption while largely maintaining streaming speed above user's normal reading speed.