If carbonating in bottles, there's not much you can do. If you get it too warm you could develop off flavors that were not there before. Keep it as close to 70F as you can and give it 3+ weeks to do it up right.
IF you wanted to drink it faster, then your only other option [really] is to keg and force carbonate. Even there you'd need to rapid force carbonate or use a stone to infuse the brew with CO2 faster.
BTW, you'll also want to chill the bottles for at least 4-5 days (7+ being better) before pouring one. IME, if you let them chill that long the sediment compacts better in the bottom of the bottle, giving a cleaner pour. Plus the CO2 has more time to get fully dissolved into the brew. Both are well worth the wait IMO.
Of course, I'm kegging now so I don't worry about sediment or waiting past the carbonation period. Two weeks after it gets placed into the brew fridge and put onto the gas feed I'm pouring pints and enjoying homebrew.