The problem can be solved by Gibb's free energy equation.
Gibbs free energy ( G), gives us the enthalpy change of a reaction, DeltaH, minus the entropy change of the reaction system, DeltaS_(sys), multiplied by the temperature of the reaction, T.
DeltaG=DeltaH−TDeltaS_(sys) (Review concept )
A positive Gibb's free energy change (DeltaG) signifies a non- spontaneous change while a negative change signifies a spontaneous one. A zero change indicates a state of chemical equilibrium at the given temperature.
To determine the threshold temperature at which a transition from spontaneous to non-spontaneous change happens, we need to determine the temperature for which DeltaG = 0
Substituting values,
-1036 * 10^3J - T (K)*-153.2 JK^(-1)= 0
=>153.2*T = 1036*10^3
=>T = 6762.40 K
So, above 6762.4 K the reaction becomes non-spontaneous.