I'm interested in the results of this, but uninterested in the sense that the results won't amount to any practical application.
The various gasses are infinitely more expensive than (free) air, and will not have significantly better operating properties.
The only way a different gas could keep the tires cooler is to more readily absorb heat, and then transfer it to the wheel. Heat conduction is the property of the gas that would be important here, and the conduction rate can be looked up for the various gasses.
That said, helium would be more dangerous since it will leak out rapidly, requiring a pressure check before each trip.
Further, each time you check the tire pressure, you loose a little bit of pressure. I wouldn't be surprised if you loose 0.5 psi each time you check a trailer tire. This, along with the other variables of heat expansion and the tire just loosing gas will muddy the results of the test, since these variables aren't tightly controlled.
I know that is a lot of negative talk about the experiment, but I'm still curious to read the results, and I think it's great that Oil Pan has the motivation to take on such a test and share the results with everyone.