FAR 23 has rules about the limits for extrapolating test data to higher or lower temps and altitudes.
They (we at times) used to do a short series of takeoff and landing tests at a place like Bacchus Marsh and a fancy (for then) computer program would print those P charts.
Charts also for climb performance limits apply to some types - remember that little line on the C150 P charts derived from a goround with flap down.
Just can't wait until an FOI rocks up for some refresher training.