For a spontaneous reaction, ΔG<0.
As per the Gibbs-Helmholtz equation, ΔG=ΔH−TΔS
When ΔH is negative, i.e., the reaction is exothermic and ΔS is positive, i.e., the disorder is increasing, the value of ΔG will definitely be negative and the process will be spontaneous for all temperatures.