Why does reactivity rise with temperature?

I was sitting by my grill and saw it rusting more where it gets very hot. I was thinking that "yeah - reactivity rises with heat". The parts made out of iron have reacted with oxygen in athmosphere.

Then i started to think why reactivity actually rise with temperature? The atoms have more velocity but they dont escape the surface. Is there some fancy quantum thing happening - where the tunneling distance propability rises with heat?