In this article, the structural stability of a metasurface absorber that works at 2.8 THz is analyzed. Since the absorber is made of metallic titanium, its elemental inclusions will be heated up and expand when absorbing electromagnetic waves. To evaluate the accumulated heat, the structural thermal expansion and the stability of the wave-absorbing performance, electromagnetism-thermodynamics-structural mechanics multiphysics simulations are conducted. Based on the thermal stability study, thermistors are further introduced into the metasurface, leading to two thermal controlled terahertz absorbers. Numerical experiments show that the absorbers present a peak absorption coefficient of 92.7% at 2.79 THz up to the temperature of 1761.4 K. When the temperature rises, the absorption frequencies of the two absorbers shift to 3.51 THz and 3.94 THz, with the peak absorption coefficients of 92.8% and 93.8%, respectively.