An AT cut crystal has a third order Bechmann curve. See attached. A given crystal has a curve based on the mechanical accuracy of the angle of the cut of the crystal blank from the large quartz bar.
Each crystal is unique (but fits a given 3rd order curve) and must be tested by at least a two temperature/frequency points to determine which curve in the AT Bechmann family it best fits.
If the crystal mount is done correctly so not to stress the quartz blank and the quartz blank is processed with good quality, it will only take two points to determine which Bechmann curve it matches. Many calibration tests take more then two temp points just to be sure and average out inaccuracies in absolute temp and freq readings.
There is likely some temp compensation via oscillator circuit temperature dependent capacitors to flatten out the curve. An ovenized oscillator relies on the temp of the oscillator/crystal environment being held constant, again usually in the 55-65 deg C range at the second 3rd order inflection point where the freq shift versus temp change is minimized.
A TCXO, like found in a cellphone or GPS receiver, has a reverse Bechmann IC that drives a varactor to warp the crystal oscillator and flatten out the frequency versus temperature.