A change in temperature has absolutely no effect upon Mach Number, Calibrated Airspeed, or Equivalent Airspeed.
A change in temperature will have a direct effect upon the Local Speed of Sound, and thus, for a given Mach Number (or CAS and EAS), TAS will change.
For a given Mach Number, TAS in Knots may be found from the formula -
TAS = 38.975 X Mach Number X Square Root of Absolute Temperature.
(Where Absolute Temperature °K = SAT °C + 273.15)
There is a side issue which may be misleading you. If an aircraft is in stable flight with a constant thrust and Mach Number, encountering warmer air will cause the Mach Number to decrease. That is entirely due to the effect of the warmer air upon Net Engine Thrust, and nothing to do with Mach number. If thrust is restored to it's original value (A new N1, EPR etc.), the original Mach Number, Mach, CAS, and EAS will all be restored, whilst TAS is higher. Colder air will have the opposite effect.
Regards,
Old Smokey