Examples of processes that are spontaneous only above or below a certain temperature
The phase transition of water from solid (ice) to liquid
H2O (s) → H2O (l)
The enthalpy of this reaction is positive since the melting of ice requires heat. The entropy of the reaction is positive since the water molecules in their liquid state have a higher degree of freedom than the water molecules locked in the crystal lattice of solid ice.
Since the Gibbs free energy is calculated by the equation ΔG = ΔH - TΔS, when the temperature is zero ΔG > 0, because if T=0 then ΔG = ΔH. This makes sense: Ice does not spontaneously melt at very low temperatures.
As the temperature increases, ΔH and TΔS will move very close to each other in magnitude until at a certain temperature ΔH = TΔS. At this point, ΔG = 0 and the reaction will be at equilibrium. This temperature, of course, is at 0 °C (273.16 K) where ice and liquid water are in equilibrium.
Once the temperature has increased beyond the equilibrium temperature ΔH < TΔS, which will make ΔG < 0. This also makes sense: Ice will melt spontaneously at temperatures higher than 0 °C.
The rusting of iron
The rusting of iron is the reaction of iron with oxygen to form ferric oxide:
4 Fe + 3 O2 --> 2 Fe2O3
The enthalpy of this reaction is negative since the reaction releases heat. The entropy of the reaction is negative since the number of molecules decreases (from a total of seven on the left side of the arrow to two on the right side of the arrow).
Since the Gibbs free energy is calculated by the equation ΔG = ΔH - TΔS, at low temperatures ΔG > 0, because the term ΔH < TΔS. As the temperature increases, ΔH and TΔS will move very close to each other in magnitude until at a certain temperature ΔH = TΔS. At this point, ΔG = 0 and the reaction will be at equilibrium.
Once the temperature has increased beyond the equilibrium temperature ΔH > TΔS, which will make ΔG > 0. At a sufficiently high temperature, the reaction stops being spontaneous.