I don't understand your premise. If an oscillator won't start, it won't start.
There are many reasons why an oscillator won't start. Some may start if you tap the crystal case or touch a probe to the circuit.
Contamination could cause nonlinearities that could hinder startup. There are many other effects that could hinder oscillation. Some have been described previously. One that has not been mentioned so far is activity dips. This is described as follows:
"Activity dips occur where the f vs. T curves of unwanted modes intersect the f vs. T curve of the wanted mode. Such activity dips are highly sensitive to drive level and load reactance."
See Vig, April 2012, Page 60
An activity dip could hinder startup at a particular temperature.
Good idea.