I don't think it's a fixed point. But more to do with VMO and MMO.
During a VNAV climb the FMC will climb at an IAS / Mach No. dependent on cost index, expected cruise level, predicted winds and mode eg ECON. MAX ANGLE or MAX rate. As you climb at a constant IAS Mach increases and when IAS equals the desired Mach No. the FMC automatically switches to a constant Mach climb. eg. if you are climbing at 280kts and the Mach No. is 0.79 the FMC will switch at the altitude where 280kts equals M0.79. As Mach is temperature dependent this will occur mostly at a specific temperature not a specific FL.
If you are climbing in Level Change or V/S then the logic is slightly different. As you climb you are initially IAS limited. eg 340kts. At sea level this equates to about 0.55 Mach. As you climb 340kts eventually equals MMO eg 0.82 Mach and as you climb further 340kts indicated will exceed MMO. Remember in the cruise we often fly at 0.79 with an IAS of 240kts or less! At the point where VMO equals MMO the aircraft becomes Mach limited. You can see this when the barbers pole or black and red bar begins to reduce. This is the point at which the MCP will change over to Mach. Again it is mostly temperature related. It usually occurs at around FL260 but is not dependent on the FL. Usually the aircraft will switch from say 280kts to M0.69 or so! To continue to climb at this will mean the IAS will begin to decrease and so it is prudent to change back to IAS until you reach your desired Mach No. and then change to Mach. If you don't the aircraft will eventually overspeed when the IAS equals MMO.
In the descent the opposite is true but I'll let you figure that out for yourselves!!