Why does it not take place at room temperature?

The reaction, $Cr_{2}O_{3}$ (s) + 2Al(s)----------> $Al_{2}O_{3}$ + 2Cr;
$\Delta $G° = - 421 kJ
is thermodynamically feasible as is apparent from the Gibbs energy value. Why does it not take place at room temperature?

The reactants are solids, so they cannot react in the present .state or at room temperature. When the temperature is elevated, reactants melt and the reaction proceeds. Therefore, a higher temperature is required.