He is also asking about the temperature coefficient of quartz crystals.
He hasn't said what the machine is doing so that leaves room to guess.
You could measure the frequency at two temperatures at the extreme range of the device's range and then assume a linear frequency shift in between those readings.
Then you know the unloaded frequency and can work out the shift in frequency from the measured frequency when a load is put on.
It would be good if he told us this stuff, but even making a bad guess brings a reply and explains a little more of the situation.
Matlab, do you feel the coating is put on the crystal that is oscillating or is it put on something else which then adds weight to the crystal and affects its oscillation? Seems like the second one would be less destructive.