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This quote comes from the FAA's "Airplane Upset Recovery Training Aid" referring to Mach stability:
"This stability can be independent of airspeed if, for example, the airplane crosses a cold front. When the outside air temperature changes, the Mach number changes, even though the indicated airspeed may not change."
Now I thought that at a constant flight level, the relationship between IAS and Mach number is independant of temperature. So if you maintain a constant flight level and constant IAS, you also fly a constant Mach number even if the air temperature changes.
But then the source document was written by senior test pilots from Boeing and Airbus, so maybe I have got it wrong??
Going back to this original question I say mach would change because it is soley related to temperature. If temp decreased, mach would increase because TAS would be constant and the speed of sound would decrease.