The heat transfer of oil is not as good as water, so larger surfaces and a larger radiator would be needed.
This is true but only if the system is running near capacity. I would guarantee a thermo cooled lister would never come near that even in hot weather. That said, there would be no evaporative cooling like with water so a fan may be needed to blow air across the drum if the runs were long enough.
If one used a car radiator the electric fan would still need to be run through a lightbulb to slow it down enough not to over cool.
An interesting thing with oil would be you could run the engine at 150oC + without problem from the oil boiling. Wont even get near it's limit till 200 degrees but that may be putting the engine oil to the test.
No idea what the mechanical effects on the engine would be other than looking at lube issues.
A power steering pump would be good for your squirter Bob. You could take out the pressure valve all together so there was nothing to block with any particles and get more flow than pressure. Put the filter on the inlet side of the pump and you'd be fine although anything in the oil after a bit of a strain through some cloth would be unlikely to worry a vane pump I think.
They run high temp in their intended use and there is nothing but some O rings to fail in the things the temp would worry.
Can bring you one or a few up when I come as well as an alternator or 3 if you have any use for them.