I think temperature deviations will not affect the indicated mach number.
I believe you are right. I looked up the formula to derive the Mach number from air data measurements, and the Mach number is indeed not affected by temperature. The formula is derived from Rayleigh's supersonic pitot equation. The total pressure behind the shock wave and the static pressure is all you need to derive the Mach number.
The temperate is only needed to obtain the TAS
Regards,
ATCast