You might want to read this thread
about dogs who almost died of CO poisoning riding in the back of a trailer. That said, I towed horses for years behind my truck with no issues but those trailers are built with better ventilation going down the road.
Do you have vent covers to prevent rain from getting.g in if they are open? Our vent used to suck road dirt in so we won't travel with it open anymore.
As for the back of the truck, it can get hot back there but many do travel with dogs in a crate in the bed, make sure you put a blanket down to protect from foot burning. I would worry about the crate getting pinched between the fiver and truck cab.
I would think your best bet would be something like this seat cover
or one of these car seats