It's improper to make such wide, sweeping statements because it depends greatly on the equipment that the lube is in.
Oils can lubricate, provide thermal transfer, provide power transfer, seal components, etc.
I completely agree that oils typically will assist in thermal transfer, regardless if that was the main intent or not.
For example, in my Dmax engine, there are oil jets that squirt oil under the piston to cool the piston. Here, the oil's main job is thermal transfer. But, in that very same engine, that's not the only job the oil does, as we'd all agree. It's also used to reduce friction. Friction is the resistance to movement. The amount of engergy needed to overcome friction is directly linked to the heat generated in that energy release. It achieves this in pressure fed bearings by providing a medium for hydraulic wedge barriers. Cooling is secondary to component separation here. Separating the components via that wedge is what reduces the friction MUCH more than the "slipperiness" of the lube if the two components were touching. But, don't forget that oil "slickness" is very important at start up BEFORE that wedge develops.
Some people may not know that oil seals will not seal well at all if the oil cannot cling to the component oposing the seal. Here, "oil" is used to provide a hydraulic bridge to close a gap. If the host metal is too smooth, it can actually cause the oil to not be able to use it's surface tention to cling to parts. No cling = no seal; be it piston rings, or power steering pump shaft seals, etc.
In other applications, like my log splitter and my ZTR mower, oil is actually used for power transfer as it's primary goal. Driving the wedge or moving the wheel motors is the goal and NOT removing heat. But that's only true in these examples.
Overall, allowing for some implied content, 440Magnum's comments were reasonable. I don't want an engine oil that rejects heat; I want an oil that assists in thermal transfer while not being grossly affected by the oxidation and chemical breakdown that extreme heat causes. I want my oil to be able to both accept and expell heat, so that it cools a part AND sends that heat somewhere else desirable.
Oil temps are governed not only by the amount of heat that is present, but also by the velocity and volume (aka flow) at which it moves past that heat. That is as much a function of the equipment design as it is the ability of the oil to absorb thermal energy.
Blah, blah, blah, right?
Here's my point: I don't think one fairly can throw out such a huge blanket statement as " ... oil's #1 job is to do ...." without describing the entire operating environment for each individual sitation and ever hope to be right, because RARE is the time that oil has only one job or one effect in the system in which it is used. Multiple fluid characteristics allow for multiple benefits, and each has to be judged at the point of application.