Why does N₂ react with O₂ to Form NO at high temperatures?
$\Delta G = \Delta H - T \Delta S$

In the case of the $\ce{N2 + O2 -&gt; 2NO}$ , $\Delta H$ and $\Delta S$ are both positive, so the reaction is thermodynamically favorable at high temperature (such as in lightning) but not at low temperature. 

If the temperature drops to room temperature after NO is formed, it is thermodynamically favorable for NO to decompose to nitrogen and oxygen.  

However, that NO is unstable at room temperature tells us nothing about the rate of the decomposition reaction.  In fact there was an interesting 40 year study showing very little decomposition of NO sealed in glass tubes over that time period.  The authors' calculations show that without a catalyst the timescale of decompsition could be $10^{29}$ years!