oil is a classical fluid lubricant, but there may be other ones; for instance water, but it has several drawbacks, such as accelerating corrosion of ferrous materials (more suited to plastic gears, I would say).
On the other hand, you can think to gaz lubrication (air journal bearing for instance) but I feel it is more suited to a situation where the lubricated surface is not involved in transient modifications (entering and exiting contact as for gears).
And you may also think about solid lubrication, for instance with specific coatings... but all seems rather strongly depending on the application...
gas lubrication is used for lighter load and higher speed, and usually for conformal type friction surfaces. Gear is non-conformal friction surfaces, which usually used liquid lubricant or grease.
I agree with our colleague Dr. Shyu, in many developing countries, Gas or pressurized air is usually used as a lubricant as in the case of air bearing, but of course there are many limitations.
Actually solid or gas lubricants are widely studied to fulfill the requirements of gear meshing, but currently mineral oil, ester or grease are still dominant. Temperature issues may be not the most important aspect when analyzing gear fatigue failures since this is depend on the application.