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In this paper, a finite time thermodynamic model of high temperature proton exchange membrane fuel cell (HT-PEMFC) is established, in which the irreversible losses of polarization and leakage current during the cell operation are considered. The influences of operating temperature, membrane thickness, phosphoric acid doping level, hydrogen and oxygen intake pressure on the maximum output power density <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>P</mi><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></mrow></semantics></math></inline-formula> and the maximum output efficiency <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>η</mi><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></mrow></semantics></math></inline-formula> are studied. As the temperature rises, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>P</mi><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>η</mi><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></mrow></semantics></math></inline-formula> will increase. The decrease of membrane thickness will increase <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>P</mi><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></mrow></semantics></math></inline-formula>, but has little influence on the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>η</mi><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></mrow></semantics></math></inline-formula>. The increase of phosphoric acid doping level can increase <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>P</mi><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></mrow></semantics></math></inline-formula>, but it has little effect on the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>η</mi><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></mrow></semantics></math></inline-formula>. With the increase of hydrogen and oxygen intake pressure, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>P</mi><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>η</mi><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></mrow></semantics></math></inline-formula> will be improved. This article also obtains the optimization relationship between power density and thermodynamic efficiency, and the optimization range interval of HT-PEMFC which will provide guidance for applicable use of HT-PEMFCs.