For the gearbox, check (a) that it has good condition fluid and (b) that it's the right stuff. Autos are ridiculously sensitive to fluid (the same stuff transfers power in the torque converter, lubricates the gears, keeps the clutch packs alive while simultaneously not making them too slippery, provides corrosion protection AND cools the whole shooting match. It HAS to be perfect) so if it looks and smells anything other than new correct grade stuff, flush your gearbox.
For the engine... I'm at a loss. I have heard some cars that impose different RPM limits depending on temperature so if it thinks the temperature is outside normal range it could cause some strange symptoms.
If you are feeling brave, locate any coolant and oil temperature sensors/switches on the engine and disconnect them. The factory ECU will compensate by using a limp home mode that is either (a) assume extreme temperature range, protect the drivetrain, impose operational limits or (b) assume sensor fault, replace with default value that allows normal operation, light up the dashboard. But the important point is that it will be constant and you will have narrowed down the cause.
Also note that fans will be triggered incorrectly, gauges won't work, the trans won't shift nicely if it's under ECU control, and it won't run properly on a cold start, so don't run it for much longer than you have to.
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