Does any known substance ignite on cooling? As the title says, I'm interested in knowing if there is any substance — or combination of substances — that ignites (or even increases its chance of spontaneous ignition) when cooled. 

I've never heard of such a thing, nor can I find it in Atkins' Physical Chemistry, but I might easily have overlooked it, since I don't know what to call it. Googling gives me information on substances that lower the freezing point or ignition point of explosives/fuels.

It seems that this should obviously be forbidden on thermodynamic grounds, but I can't quite rule out a phase change allowing such behaviour, for instance.
Actually... yes! Iron(II) oxide is thermodynamically unstable below $848~\mathrm K$. As it cools down to room temperature (it has to do it slowly) it disproportionates to iron(II,III) oxide and iron:

$$
\ce{4FeO -&gt; Fe + Fe3O4}.
$$

The iron is in a form of a fine powder, which is pyrophoric (it may catch a fire when exposed to air). You can see it in action here.