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In order to explore the effect of external temperature $T$ in quantumcorrelation we compute thermal entanglement and thermal discord analytically inthe Heisenberg $X$ $Y$ $Z$ model with Dzyaloshinskii-Moriya Interaction term${\bm D} \cdot \left( {\bm \sigma}_1 \times {\bm \sigma}_2 \right)$. For thecase of thermal entanglement it is shown that quantum phase transition occursat $T = T_c$ due to sudden death phenomenon. For antiferromagnetic case thecritical temperature $T_c$ increases with increasing $|{\bm D}|$. Forferromagnetic case, however, $T_c$ exhibits different behavior in the regions$|{\bm D}| \geq |{\bm D_*}|$ and $|{\bm D}| < |{\bm D_*}|$, where ${\bm D_*}$is particular value of ${\bm D}$. It is shown that $T_c$ becomes zero at $|{\bmD}| = |{\bm D_*}|$. We explore the behavior of thermal discord in detail at $T\approx T_c$. For antiferromagnetic case the external temperature makes thethermal discord exhibit exponential damping behavior, but it never reaches toexact zero. For ferromagnetic case the thermal entanglement and thermal discordare shown to be zero simultaneously at $T_c = 0$ and $|{\bm D}| = |{\bm D_*}|$.This is unique condition for simultaneous disappearance of thermal entanglementand thermal discord in this model.

Thermal Entanglement and Thermal Discord in two-qubit Heisenberg XYZ Chain with Dzyaloshinskii-Moriya Interactions