Automatic Heuristic Design (AHD) is an effective framework for solving complex optimization problems. The development of large language models (LLMs) enables the automated generation of heuristics. Existing LLM-based evolutionary methods rely on population strategies and are prone to local optima. Integrating LLMs with Monte Carlo Tree Search (MCTS) improves the trade-off between exploration and exploitation, but multi-round cognitive integration remains limited and search diversity is constrained. To overcome these limitations, this paper proposes a novel cognitive-guided MCTS framework (CogMCTS). CogMCTS tightly integrates the cognitive guidance mechanism of LLMs with MCTS to achieve efficient automated heuristic optimization. The framework employs multi-round cognitive feedback to incorporate historical experience, node information, and negative outcomes, dynamically improving heuristic generation. Dual-track node expansion combined with elite heuristic management balances the exploration of diverse heuristics and the exploitation of high-quality experience. In addition, strategic mutation modifies the heuristic forms and parameters to further enhance the diversity of the solution and the overall optimization performance. The experimental results indicate that CogMCTS outperforms existing LLM-based AHD methods in stability, efficiency, and solution quality.