To start of, a Jolly Tyrunt/Tyrantrum is one of the best natures to get, so you don't have to worry about the nature hurting you.
In concern to IV's, you will definitely want to train the Tyrantrum with the all 31 IV but SpDef. If you look at Tyrantrum's base stats, it has great Atk/Def, moderately good HP/Spd, but very low SpAtk and SpDef. So, even if you had a 31 IV in SpDef, your SpDef stat at lvl100 will not even cross the 200-stat mark, since there's no benefit in training it's SpDef EV, as well as having a nature that has no effect of SpDef anyways. So, not having a Tyrantrum with 31 SpDef IV will not hurt it whatsoever. So, definitely train this Tyrunt with EV's mixed around in Atk/Def/Spd, and you'll have one heck of a Tyrantrum.
In concern to the Tyrantrum with the 31 IV's attack, unless the actual IV for attack is ~25+, it will not be any better than the Tyrantrum will lower SpDef IV - and you do want to have a Tyrunt with great Atk since it's its best base stat.
Hope I helped! :)