Has there been any experimental measurement of the temperature and pressure gradient across the Kármán line? How much time did it take for a space shuttle (such as Atlantis) to cross it, and whether it is the most critical zone during re-entry?
Just so you are aware - the Kármán line is not a physical thing. It is an imaginary boundary, that gives a rough, easy to remember height for the border between Earth and space of 100km (although according to Jonathan McDowell, that imaginary border may be wildly incorrect, and need to be revised inwards to 85km)
There is no specific pressure or temperature gradient across it, in fact the atmosphere varies in height depending on time of year, solar weather, and even location above the earth, so while the temperature increases below the line, it is not specific, and if the line needs to be moved closer to the Earth then any calculations would need to be revised again.
The Kármán line is not one of the regions that concerns astronauts. It is worth reading the Kármán Line Wikipedia page, in order to understand.