For a reaction to be spontaneous at all temperatures, the change in Gibbs free energy ($\Delta G$) must be negative ($\Delta G < 0$). According to the Gibbs free energy equation, $\Delta G = \Delta H - T\Delta S$. If $\Delta H < 0$ (enthalpy decreases) and $\Delta S > 0$ (entropy increases), then the term $-T\Delta S$ becomes negative (as $T$ in Kelvin is always positive). Consequently, $\Delta G$ will always be negative regardless of the magnitude of temperature, making the reaction spontaneous at all temperatures .