Originally Posted by FE Hoppy
the TAS difference will give us a higher gradient.
No, that is not correct. The lower temperature will give you a lower TAS and a lower rate-of-climb. The gradient is not changed by TAS, it depends on the thrust-to-weight ratio and that is equal for the assumed and the actual temperature because you set the same thrust.
Likewise, the acceleration in terms of kts TAS per second does not change, the number of seconds changes and therefore the distance.