Large Language Models (LLMs), such as GPT models, are increasingly used in software engineering for various tasks, such as code generation, requirements management, and debugging. While automating these tasks has garnered significant attention, a systematic study on the impact of varying hyperparameters on code generation outcomes remains unexplored. This study aims to assess LLMs’ code generation performance by exhaustively exploring the impact of various hyperparameters. Hyperparameters for LLMs are adjustable settings that affect the model’s behaviour and performance. Specifically, we investigated how changes to the hyperparameters—temperature, top probability (top_p), frequency penalty, and presence penalty—affect code generation outcomes. We systematically adjusted all hyperparameters together, exploring every possible combination by making small increments to each hyperparameter at a time. This exhaustive approach was applied to 13 Python code generation tasks, yielding one of four outcomes for each hyperparameter combination: no output from the LLM, non-executable code, code that fails unit tests, or correct and functional code. We analysed these outcomes for a total of 14,742 generated Python code segments, focusing on correctness, to determine how the hyperparameters influence the LLM to arrive at each outcome. Using correlation coefficient and regression tree analyses, we ascertained which hyperparameters influence which aspect of the LLM. Our results indicate optimal performance with a temperature below 0.5, top probability below 0.75, frequency penalty between -1 and +1.5, and presence penalty above -1. We make our dataset and results available to facilitate replication.