A change in temperature does not change pitot (P) or static (S) pressures and

MN = (P – S)/S so MN is constant.

 

Furthermore:

 

CAS is a measure of dynamic pressure = ½ρV2

Where ρ = air density (decreasing as temperature increases) and V = TAS (increasing to keep CAS constant)                                                                       

 

Also:

 

TAS = MN x LSS = Constant x Increasing = Increasing.