Check out your whiz wheel. CAS (IAS) vs Pressure altitude gives a constant mach number. You are correct that the mach number varies with temperature but so does the air density. So if temp increases = density decreases = the aircraft has to move faster through the air to achieve the same amount of lift (TAS increases) but the IAS and mach number remain the same at a constant level.
I don't think I've explained that very well but I hope it helps in any way.
Edit: It might help to think of IAS as a value that represents the relative force of the air hitting the wing rather than a speed.