Looking for alterable metamaterials, whose electromagnetic properties can be dynamically and real-time controlled, has attracted a great attention recently. In this paper, we present a numerical study of thermo-tunable polarization-insensitive fishnet metamaterials operating at THz regime. The conventionally used metal is replaced by InSb in which the temperature-dependent conductivity plays a key role in tuning the left-handed frequency. By increasing the temperature of the InSb patterns from 300 to 350K, we show that the left-handed transmission peak can shift from 0.8 to 1.1THz and fractional bandwidth of the negative refractive index goes from 14% to 22%. Thermally increased carrier density of InSb is found to be the reason for the enhanced magnetic resonance and stronger left-handed behavior in addition to the tunability. The equivalent LC circuit model and standard retrieval method are performed to elaborate our proposed idea.