Mach Number can be determined
solely from measurements of dynamic (ie Pt-P ... say, CAS) and static pressure (P .. say, pressure height) .. temperature doesn't come into it at all.
There's probably not much point in quoting this and that form of equations as they tend to confuse those who aren't used to playing with them .. however, most of the standard engineering texts will provide endless arithmetic confusion for those who might wish to flagellate themselves mercilessly ....
This
thread has a few more thoughts ...