On our current Class C, I used Dual Lock tape and mounted it where you were thinking, under the overhang, behind the cab doors. Even on the shade side, even at night, it read about 5 degrees high. I think it was getting some heat passing through from the interior.
I like the ideas of the LP compartment if you want a true reading, or the wet bay if you want to monitor that. I'll do one of those from now on. Yes, the smartphone tells me the outside temp anyway.
Dual lock tape is ideal for this type of thing. Like velcro, you can remove the object, but it's much more solid than velcro.
Example