# Gibbs Free Energy: Exothermic, low temperature & reduced system entropy - such reaction is spontaneous or not?

According to $\ce{\Delta G^\mathrm{o}= \Delta H^\mathrm{o} -T\Delta S^\mathrm{o}}$, if a reaction

a) is exothermic,

b) reduces system entropy, and

c) the temperature is low,

then it is spontaneous.

Consider the combustion of hydrogen gas, with $$2\ce{H2}+\ce{O2}\to 2\ce{H2O}.$$ This reaction is exothermic, and the system's entropy decreases. So does it mean that:

1) this reaction is spontaneous at low temperatures?

2) this reaction is not spontaneous at high temperatures?

If so, it seems counter-intuitive that placing the reagents in a high-temperature environment will not cause spontaneous combustion. Can you explain why this should be the case?