Peat fire is much like gunpowder fire, just much slower. Peat naturally accumulate nitrates (saltpeters among others) which are essential in the gunpowder burning process.

As an evidence, I'd like to present a study that proves that peat emits NO2: https://www.jstor.org/stable/2845931?seq=1

This is why peat can burn underground without much access to oxygen. And, burning underground, it does not need much external heat.