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In practical applications, rapid prediction and optimization of heat transfer performance are essential for premixed methane impinging flame jets (PMIFJs). This study uses computational fluid dynamics (CFD) combined with a methane detailed chemical reaction mechanism (GRI–Mech 3.0) to study the equivalence ratio (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϕ</mi></mrow></semantics></math></inline-formula>), Reynolds number (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi></mrow></semantics></math></inline-formula>) of the mixture, and the normalized nozzle–to–plate distance (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><mo>/</mo><mi>d</mi></mrow></semantics></math></inline-formula>) on the heat transfer performance of PMIFJs. Moreover, the Kriging model (KM) was used to construct a prediction model of PMIFJ heat transfer performance. A genetic algorithm (GA) was used to determine the maximum likelihood function (MLE) of the model parameters for constructing KM and identify the points with the maximum root mean square error (RMSE) as the new infilled points for surrogate–based optimization (SBO). Combining these methods to analyze the simulation results, the results show that the global heat transfer performance of PMIFJs is enhanced with the increase in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϕ</mi></mrow></semantics></math></inline-formula>, the increase in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi></mrow></semantics></math></inline-formula>, and the decrease in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><mo>/</mo><mi>d</mi></mrow></semantics></math></inline-formula>. Sensitivity analysis points out that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϕ</mi></mrow></semantics></math></inline-formula> significantly affect enhanced heat transfer, while <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><mo>/</mo><mi>d</mi></mrow></semantics></math></inline-formula> has a relatively small effect. In addition, GA was also used to search for the optimal heat transfer performance, and the global heat transfer performance at specific conditions was significantly enhanced. This study deepens the understanding of the heat transfer mechanism of impinging flame jets and provides an efficient method framework for practical applications.