<p>An intriguing interaction of axions, which are naturally expected to be light and weakly interacting due to their shift symmetry, is their coupling to the Higgs boson. This interaction has significant implications for the electroweak phase transition and could facilitate electroweak baryogenesis. By incorporating a temperature-dependent axion potential arising from Higgs thermal fluctuations, we investigate how the axion-Higgs coupling modifies the electroweak phase transition. Furthermore, we explore the cosmological aspects of axions, including their cosmic evolution, thermalization processes, and their potential role in dark matter production.</p>