The spontaneity of a reaction can be predicted by the amount of Gibbs free energy. If it is negative, then the reaction is spontaneous. The reaction for Gibb's energy is
ΔG=ΔH-TΔS, where H is the enthalpy, T is the temperature and S is the entropy.
If the reaction favors low temperature, the enthalpy must be negative so that it will yield a negative ΔG. In other words, an exothermic reaction is spontaneous even at low temperatures. Also, the reaction could still be spontaneous if entropy is high, meaning, the system is not in order.
