(a) Mach can be expressed as an equation involving only pressures etc ... with no temperature term. Crossover height not related to OAT.
The idealised flow equations (see just about any old garden variety aerodynamics text) give -
Pt/P = (1 + (g-1)/2 * M^2)^(g/g-1)
where g = 1.4, typically.
(b) From jtr's post and (a), the climb IAS/climb IMN combination determines the pressure height at which the two coincide - ie the "crossover height".