HoMM3 HD is a mod (add-on) for the game Heroes of Might and Magic 3.

That would be ideal... At least, having such an option.

1) - in my opinion, this is essential for tournaments and/or players who aren't as quick-witted (I, as an example of such a player, often lose clarity/planning under a chess timer because it's a permanent time crunch), but
2) - this undermines the very slogan of Quick Play ("Speeding up the game")
Ideally, there would be another setting in the timer, from 1 to 5 minutes, possibly a function based on game time. But I'm sure everyone would be against it.
And I can't resist: the lobby is a sweetheart © Colonel Monblan.
*as an alternative, increase the turn time in Quick Play by 30..45 seconds.
There will still be savings, even if you increase it by 2 minutes, even by 7 - this is the minimum turn duration for an opponent.