Airbus Error,
Respectfully suggest that you revisit Kermode ... or, better still, any of the standard undergrad basic aerodynamics course texts ... Kermode is a bit simplistic for other than a generalist overview approach to life .... indeed your examples, for instance, must unsettle your position ... the mach number quoted is the same for both temperatures (M=1) .. although the OAT is drastically different ..... this would seem to indicate that mach is not terribly interested in the OAT.
Speed of sound, however, certainly depends on temperature -
a/a0 = root(T/T0) with temperatures in degrees absolute ...
Mach, however, is not interested in temperature ....
Very common misunderstanding ...
Mach compares static and dynamic pressures. The equations are certainly different ... but the ASI and the machmeter are, in fact, doing similar sorts of things ...