One aspect that stands out in my mind is that there would be no shock wave in front of a paper airplane... assuming standard "dart" folding. Therefore, no matter what speed, the heat build up would be greater than can be dissipated and the plane would simple turn to ash as fast as it could enter the upper atmosphere. I don't think that there would be enough structural strength to withstand a "flaring" manoeuvre and the plane would always present a knife edge as it fell toward the earth.
I found a very interesting document on the FAA website, on re-entry design...
https://www.faa.gov/other_visit/avia...om%20Space.pdf