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A thermally tunable terahertz metamaterial absorber (MA) with InSb embedded in a metal-dielectric-metal structure is proposed. The transmission and tuning properties of the proposed metamaterial absorber are analyzed for the temperature ranging from 160 K to 350 K. The simulated results show that the maximum absorption of the absorber is nearly 99.8% at a full-width at half-maximum (FWHM) of 38 GHz, and the absorption frequency can be dynamically tuned from 0.82 THz to 1.02 THz.