Wow! I've had them parked in some pretty hot places (Yuma, Arizona -
sometimes as hot a 120°F, ~50°C with internal temps much hotter than that),
but I have never had a firewall mat burn. I have certainly had them rot.
I wonder if there were mouse droppings or urine involved. That could give
enough bioactivity for spontaneous combustion. Or maybe drying oils (linseed,
or tung oil, for example) that undergo slow oxidation in the air.
Other than that the only thing I can imagine is some kind of spark or other
external ignition, like from a cigarette.

Some of the glass cleaning liquids might help get the sticky stuff off.
My 122 wagon sometimes has a peculiar burning smell but I haven't found
any evidence of combustion.
--
George Downs Bartlesville, Heart of the USA!