I see you are from Illinois, next door to us Indiana Hoosiers! Hi neighbor!
It sounds like you are living in good old farm country, where pole barns and pole shelters are common places to store farming equipment. Pole barns and pole shelters were a cheap and economical way to create a cover for farming machinery without having to build a solid walled structure.
In all the 62 years of my life, (and most of that living in Indiana), I've never know where heat inside these shelters ever caused a problem on anything stored under them. If you have air flow between the top of the camper and the roof of the shelter, I don't think there is anything to be concerned about (except, maybe, birds attempting to build nests in the rafters of the shelter). As far as the roof of the RV, they are made to withstand heat and cold. Heat and cold won't hurt them. It's the sun and UV that causes deterioration.
Many people store their RV's in enclosed barns (where I live especially) and you know the heat builds in those aluminum sided and aluminum roofed buildings! Does't seem to hurt their RV's at all.
You are fortunate to have a cover! Enjoy and don't worry about anything (except birds).