Dennis,

The propensity of an organic oil such as olive oil to self-heat is dependent mostly upon its fatty acid content. The oxidation of these fatty acids is the exothermic reaction that, in the right circumstances, can lead to ignition.

Olive oil is composed mostly of oleic acid. The rest of the oil consists of hexadecanoic acid, and minor amounts of other C16 and C18 fatty acids.

Oleic acid has only one double bond to oxidise, and hexadecanoic acid is fully saturated. Olive oil therefore has quite a low tendency to self-heat.

But while the tendency to self-heat on its own is quite low, it is quite possible for these kinds of oils to spontaneously combust if supplied with enough heat from an external source (e.g. heated textiles removed from a dryer or a hot fixture nearby).

As mentioned by Steve, Stauffer's article (published in 2 parts) is the most comprehensive reference in the field on this topic. The Ignition Handbook also goes into detail. There are papers that cover the fire debris analysis aspect of self-heating oils (co-authored by Reardon), but nothing specific regarding olive oil. "DSC determination of thermally oxidized olive oil" (2003) by Vittadini et al. goes into some detail about the autooxidation of olive oil also.