We introduce Enhancing Graph of Thoughts (EGoT), a method designed to enhance the performance of large language models (LLMs) on complex reasoning tasks. EGoT automates the process of generating accurate responses using given data and a base prompt. The process consists of several steps: It obtains an initial response from the answering node using the base prompt. Evaluation node evaluates the response and generates reasoning for it, utilizing the score's probabilities to enhance evaluation accuracy. The reasoning from both the answering node and the evaluation node is aggregated to identify the problem in the response. This aggregated reasoning is incorporated into the base prompt to obtain an enhanced response. These steps are organized in a graph architecture, where the final leaf nodes are merged to produce a final response. As the graph descends, the temperature is lowered using Cosine Annealing and scoring, to explore diverse responses with earlier nodes and to focus on precise responses with later nodes. The minimum temperature in Cosine Annealing is adjusted based on scoring, ensuring that nodes with low scores continue to explore diverse responses, while those with high scores confirm accurate responses. In sorting 256 elements using GPT-4o mini, EGoT performs 88.31\% accuracy, while GoT (Graph of Thoughts) achieves 84.37\% accuracy. In the frozen lake problem using GPT-4o, EGoT averages 0.55 jumps or falls into the hole, while ToT (Tree of Thoughts) averages 0.89.