The power limit does two things, well really one.
It lowers the power level the gpu chip on the card and consume and use.
As you said it should be cooler.
But if you start to overclock the Gpu and the memory of the card the faster you ask both to work in Mhz the more power it will require to prevent the Gpu from crashing under heavy load usage, intern more voltage can produce more heat output.
Now I am not sure so don`t quote me on this, it could also be the case that when you lower the cards gpu down to -96Mv
it may cap the maximum usage or utilisation of the gpu core.
For example it might only let the gpu core reach a maximum of 80% gpu utilisation to control power, as I said if it was only working at a maximum of 80% it would require less power over 99% utilisation of the gpu core.
Is the card running hot for you, if so what temps are you getting at Idle and full Gpu load ?
And how long have you had it, I only ask because it seems you have heat concerns when running the card to ask a question like you are asking Rafab_21.