In this study, a perfect metamaterial absorber (PMMA) based on an indium antimonide temperature-sensitive material is designed and investigated in the terahertz region. We demonstrate that it is an ideal perfect narrow-band absorber with polarization-insensitive and wide-angle absorption properties. Numerical simulation results show that the proposed PMMA can be operated as a temperature sensor with a sensitivity of 21.9 GHz/K. A graphene layer was added to the PMMA structure to improve the sensitivity, and the temperature sensitivity was increased to 24.4 GHz/K. Owing to its excellent performance, the proposed PMMA can be applied in thermal sensing, detection, and switching.