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We analyzed the transverse momentum spectra of positively and negatively charged pions (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>π</mi><mo>+</mo></msup></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>π</mi><mo>−</mo></msup></semantics></math></inline-formula>), positively and negatively charged kaons (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>K</mi><mo>+</mo></msup></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>K</mi><mo>−</mo></msup></semantics></math></inline-formula>), protons and antiprotons (<i>p</i> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>p</mi><mo>¯</mo></mover></semantics></math></inline-formula>), as well as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϕ</mi></semantics></math></inline-formula> produced in mid-(pseudo)rapidity region in central nucleus–nucleus (AA) collisions over a center-of-mass energy range from 2.16 to 2760 GeV per nucleon pair. The transverse momentum of the considered particle is regarded as the joint contribution of two participant partons which obey the modified Tsallis-like transverse momentum distribution and have random azimuths in superposition. The calculation of transverse momentum distribution of particles is performed by the Monte Carlo method and compared with the experimental data measured by international collaborations. The excitation functions of effective temperature and other parameters are obtained in the considered energy range. With the increase of collision energy, the effective temperature parameter increases quickly and then slowly. The boundary appears at around 5 GeV, which means the change of reaction mechanism and/or generated matter.