Does any known substance ignite on cooling?
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.