The last part of the cigar right before it gets hot and harsh is usually everyones favorite part!

You may be talking about the hot harshness that signals it's time to let the smoke go out. That usually hits at the last 1/4 mark. There's nothing to do at that point but let it cool more between puffs and take shorter puffs if you're tenacious like that, or let it die a dignified death and remember it fondly.