>It's a strong vibration.
>It seems to come from the front half of the car.
>It appears only when the motor is hot, only above 2500 rpm and while
>It stops when I stop accelerating, even if I keep the same speed.
>It does not appear when I am pushing on the gas pedal without any gear
>engaged: the motor turns perfectly round.
First thing that comes to mind with that description is a broken motor mount.
Load the engine up against the transmission, let it get up into the power band,
and it promtly cocks over. But since there's no load while in neutral, it
doesn't move when you rev it then.
The second thing that comes to mind is something having shifted or broken on
engine that is contacting the body or frame when the engine cocks a little from
load without a broken motor mount.