This paper presents an innovative design integrating micro-perforated plate (MPP) with P-type triply periodic minimal surfaces (TPMS) to enhance sound absorption capability, particularly at high temperatures. Two theoretical models based on the Johnson–Champoux–Allard–Lafarge model and the dual-cavity parallel theory are proposed for predicting sound absorption coefficients. The two models yield highly consistent results, which are cross-validated by simulation and experiment. A systematic investigation of impedance and absorption correlation is conducted through simulated contours, revealing the underlying mechanisms governing thermo-viscous energy dissipation. The findings indicate that energy dissipation mainly relies on viscous dissipation arising from the friction between MPP and sound waves, whereas thermal losses generated by TPMS interaction with sound waves are negligible. As temperature rises, increased air viscosity leads to higher acoustic resistance, greatly enhancing the absorption peak and half-absorption bandwidth. By integrating subunits with different resonance frequencies, a low-frequency broadband structure is developed, achieving outstanding sound absorption (α > 0.85) within 576–877 Hz, and this absorption bandwidth is further expanded to 930–1608 Hz with temperature increases, representing a 125% increase in bandwidth, demonstrating that the temperature effect positively enhances the absorption bandwidth. This work provides critical guidelines for designing sound-absorbing metamaterials for high-temperature purposes.