High-temperature reactions widely exist in nature. However, they are difficult to characterize either experimentally or computationally. The minimum energy path (MEP) model routinely used in computational modeling of chemical reactions is not justified to describe high-temperature reactions since high-energy structures are actively involved at high temperatures. In this study, we used methane (CH₄) decomposition on Cu(111) surface as an example to compare systematically results obtained from the MEP model with those obtained from an explicit sampling of all relevant structures via ab initio molecular dynamics (AIMD) simulations at different temperatures. Interestingly, we found that, for reactions protected by strong steric hindrance effects, the MEP was still followed effectively even at a temperature close to the Cu melting point. In contrast, without such protection, the flexibility of the surface Cu atoms could lead to a significant reduction of the free-energy barrier at a high temperature. Accordingly, some earlier conclusions made about graphene growth mechanisms based on MEP calculations should be revisited. The physical insights provided by this study could deepen our understanding of high-temperature surface reactions.