Minimizing frequency drift in LM331
The temperature coefficient of the capacitor can have a profound effect on the accuracy and stability of the output. This is what the other thread that you quoted is referencing.

However, some of you data seems to suggest that you are getting noise into your circuit or that your input reference voltage has some fluctuation or that your method for measuring the frequency has some instability. If you haven't already done so, you should assess these error terms.

You may find it helpful to determine the Hertz/Volt transfer ratio and assess your variation in light of this. You may find that the output frequency variations may account for a very small input fluctuation. This could help you to track down the cause of the fluctuations.