Well it depends on what Roosevelt does about World War One. Does TR enter the war after the Lusitania or a similar ship with US passengers sink? Does he enter immediately in 1914? Does he lead an effort for peace talks in the beginning months of the war, potentially defusing the whole thing? Or does he wait until after the 1916 election to enter the war?
There's so many possibilities for how World War One would be different under a Roosevelt presidency, so it's hard to imagine the election without details.
Yeah, there might not even be a war in the first place. Teddy had considerable clout with European leaders, especially those of Germany & Britain. With his 1906 Nobel Peace Prize as a credential, he likely could've offered to mediate the problem between Austria-Hungary & Serbia, & his prestige with Germany & Britain in particular likely would've made that happen. In that event, we're talking about a negotiated settlement; I'd guess wildly that the terms might've been very roughly the same as those all-but-accepted by Serbia in real life, the ultimatum notwithstanding.
To get back to the original question, he'd certainly seek another term in 1916, & he'd win: given TR's overwhelming popularity, the Democrats would've likely been in disarray & would've either turned to a dark horse or a retread (Bryan?) as a sacrifical candidate.
