Keeping it 'simple' for ppppilot.
MCP flies you at IAS. Let's say 280kts?
2 things are happening as you climb
1) At 280kts IAS, your TAS is increasing
2) Local Speed of sound ('TAS') is reducing
Thus, a 280kt IAS climb in your 737 to 41000 feet will have you flying at around Mach 1.0 when you get there, starting at around M0.4 at sea level. As a rough guide, the S of S at 41000 is roughly 580kts ('TAS'). I don't know what 280kts IAS at 41000' is, but I guesss.....around 580kts....?
As said above, 'official' change over is quoted as 26000' but that depends on air mass and selected speed.