  By using geometric measure of discord (\texttt{GMOD})[Phys. Rev. Lett, 105,
109502 (2010)] and measurement-induced nonlocality (\texttt{MIN})[Phys. Rev.
Lett, 106, 120401 (2011)], we investigate quantum correlation of a pair of
two-level systems, each of which is interacting with a reservoir at finite
temperature $T$. We show that, for a broad class of states of the system,
\texttt{GMOD} and \texttt{MIN} can endure sudden death, and there is no
asymptotic decay for \texttt{MIN} while asymptotic decay exists for
\texttt{GMOD}. We also give the dynamics of \texttt{GMOD} and \texttt{MIN} with
respect to the temperature and illustrate their different characteristics.
