Veggy oil will spoil when exposed to air for a long period of time...pretty stupid if u ask me.
We don't now if that is vegitable oil or something else though. There are a number of different oils that will do the job. Mineral oil is a good option.
As for cooling the oil off. It shouldn't be a problem, the large surface area of the tank should disapate the heat just fine from the oil. It will warm up, but not to anything extreme.
The biggest problem is keeping the oil moving. You have to keep it moving in the tank, which he did by leaving the fans on. If you go passive you have to do something else to keep the oil moving. Otherwise the oil around the hot components heats up and stops cooling. The oil is too think for the natural convection to move it around enough.
If you really wanted to, the best solution would be to do a similar setup, but use a pump to move the oil around. I would probably even hook the pump up to some tubing and and external radiator just to keep the oil extra cool, though that would be more for some extra show than actual cooling. Common water cooling parts should do the job just fine, but the flow will be a lot lower because of how think the oil is.