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The cabin heat won't bother them, the humidity will. Lasers these days are better about stirring and drying the toner in the cartridge, but like all electrostatic copiers (i.e. Xerox machines) a highly humid environment will interfere with the static charge/transfer.
And of course the high impulse power draw while the fuser section is operating may be more than some inverters can supply.
Many of the HP inkjets are using cartridges with a "counter" built in. After so many pages, they go dead whether there is ink in them or not. and they can't be refilled, because the counter says they've been used up. Which also means that if you're stuck somewhere and the carts you need aren't on the shelf, you're totally SOL.
So for a traveler it might pay to buy an NCR refill kit (<$20 at WalGreen's) and see what make and model printers you can use it with. There are many that aren't "protected" as meanly as the HPs. Refill kits are messy, but if you aren't staying near an "inks-r-us" store....they can be useful.