Yes There are two different processes being discussed. When the hay in a barn or compost heats up it is due to thermophyllic bacteria or fungi. Without those critters it wouldn't happen. And the process in order to work needs a certain balance of nitrogen and carbon containing material. So piss on some rags and put them in a pile and you might get some heat but just wet rags won't work. Once the temperature and and volume reach a critical mass the oxidation of simple hydro carbons (like methane) take over and the living critters that started the process get fried. Eventually (as in a barn fire) the heat gets to the point all the hydrocarbons start to burn. Varnish soaked rags are strictly chemical reactions (no living critters involved).
Yeah I have tried high nitrogen fertilizer (30-10-10). I found it doesn't produce as good results as 10-10-10. No real proof of that other than how it seems to work better in the garden. Typically in the spring I can take a half a dozen bales of hay and a half pickup load of wood chips/bark/sawdust and if I get the mix just right I can turn it into nice black compost in about 10-14 days (turning it over every 3-4 days).
-jim