Calculate the minimum temperature, in kelvin, at which the reaction is spontaneous?

When a system is at equilibrium, its Delta G = 0. At any temperature in one direction from the equilibrium temperature, the reaction will be spontaneous, and at any temperature the other side of that equilibrium temperture, the reaction will be non-spontaneous. Both Delta H and Delta S are relatively temperature independent. So, using the equation

Delta G = Delta H - T Delta S, and setting Delta G = 0 will allow you to calculate the temperature at which the reaction is in equilibrium. From the wording of your title, even a very slight increase above this will cause the reaction to be spontaneous.