I have driven several 1000+ miles trips in 100°F temps in a fully loaded Dodge Grand Caravan with the 3.8 using 5w-20. Never had an issue with it.
I would just keep using whatever you are using.
Only reason to go to a 30 wt is if there is trailer towing involved.
I would be more worried about the transmission fluid condition, and just overall vehicle condition.
Interesting that Hyundai recommends 3 different oil weights. I would review the owners manual again. Those different weights are probably recommended for different climates and driving conditions. As for brand, I am one of those people who believe that branding does not make much of a difference. The most important thing is to make sure that your choice of oil meets your OEM spec.
Hyundai recommends oil based on the old style temperature chart, but does have a little caveat of the "for best fuel economy use xw-xx oil" depending on the motor, it could be 5w-20 or 5w-30.