@Ian, Answer: Try to fly PSS 777 (Fs2004). No such things working in CaptainSim 777.

No matter you enter a flex-temperature or you choose a Thrust TO/TO-1/TO-2, Climb or other setting. Nothing will change in the CS777.
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Must edit this: With PW-Engines no changes can be seen, but with GE-Engines I found out, changes are can be seen on FMC and EICAS.
So it depends on the choosen airplane?!
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Try this: Change the settings in FMC for Temperature, choose on the N1-Page different Thrusts like Crz. Climb, TakeOff and so on. You will see, the value in the top line of the FMC will not change, also the values on EICAS will not change. The CS777 AT-System is absolute wrong and not working. Philosophical question, can something be wrong if it is not working?

Solution: Use the Thrust-Levers, do not use the AP until the another company 777 will be released ;D. (Some names are changed to "other", for example Precision Manuals Development Group)

@A, if you choose the AT-Button it is working as the Speed-Button and the airplane slows down. In real this Button is no speed button, so this is wrong implemented. Maybe the programmers never saw a real B777 Cockpit before and didn´t know it.

To find a way to fly a climb with autopilot ON I tried this and it works fine:
ZFW 170000 kg, Fuel 80000 kg.
Take Off I set the N1 (GE) with the Throttles to the calculated value from the FMC.
Below 5000 ft I try to fly 220 Knots only. So with AP ON I set V/S 4000 to 5000 ft and the Speed in the Speedwindow to 220 knots.
At 1500 ft AGL I change to V/S 2500 ft/min.
At 10000 ft changing Speed to 315 Knots and V/S 500-1000 ft/min, before reaching 315 knots changing V/S to 2500 V/S
Below 17000 ft I choose V/S 2500 ft/min
From 17000 ft up to 30000 ft I use V/S 2200, later 2000 ft/min.

With CS777-200 GE LR, not tested with other airplanes. The combination between V/S and Speed prevents to overstress the engines.