.. how temperature doesn't affect CAS/MACH crossover?
You have part of the story under control ..
(a) speed of sound - a = a0 √[T/T0] - depends on OAT
(b) Mach is a function of altitude and CAS. The following might be a tad convoluted because of the limitations of presentation .. however, if you transcribe it to paper it shouldn't be too difficult to see the details (assuming my bracket counting capabilities are OK) ...
(M^2)/5 = [1/δ [(1 + 1/5(Vc/a0)^2)]^3.5 - 1 ] + 1]^(1/3.5) -1
... if you define two of these variables, the equation gives you the other, independent of OAT
... the CAS/MACH crossover. It always occurs at the same altitude
.. providing we are looking at the one pair of CAS/M values.