"Unfortunately or not I have no problem killing pests not found on the endangered lists who don't pay rent."
The problem is, not so much, killing a rodent. The problem is a poisoned rodent dying inside your camper walls or under your floor, or inside a heat or air conditioner duct. A rotting mouse smells horrible and you absolutely cannot tell where the dead mouse is actually located. And, even if you could, you'll have to tear something apart in your camper to get the dead critter out.
We had dead mouse in our bathroom wall in our home. I could never figure out where it came from. 2 years we smelled that nasty thing. I ended up remodeling that bathroom (made it bigger, knocked out a wall, re-plumbed, re-wired, new everything from studs to finished paint. I found the mouse in the process! Needless to say, I sealed up all those walls while the studs were exposed.
What I'm saying is, you DO NOT want a dead mouse trapped in the structure of your camper.
And ... to answer your question ... of course a temperature controlled environment would be more beneficial for your camper. But it's not necessary.