Several people have explored in timelines and posts what might have happened had FDR not run in 1940, and there was a depressing timeline in the old UseNet news group about FDR not even surviving the assassination attempt. Garner doesn't do the New Deal and everything's bad.
I don't think anyone's done for this that I've seen, though. What if that assassination attempt only injures Roosevelt. He can give his inaugural address on March 4th though he is clearly still a bit weak, he does all he does and America is on its way back slowly, all the jobs programs there, the military is being slowly built up, and so on. But, his health is just worse enough that he considers not running, or at least knows he might not make it past 1937 or 38 and so he better dump Garner because his heart is weaker.
If he steps down, who runs in his place? I suppose Al Smith as possible though I think he was a bit older, but he might do for a one-termer who can them continue much of Roosevelt's work.
Or, does Roosevelt gamble on himself but still dump Garner and figure that like in 1945 he will just select someone who he knew would be a good president. Obviously, that couldn't be Smith. I'm not sure who it could be, I suppose Cordell Hull. It would have to be someone who would support the New Deal wholeheartedly and that wasn't Garner, plus Roosevelt could use the excuse that he would be 70 and in as bad as shape as him anyway. I presume Roosevelt has the Democrats so enamored with him that he could choose pretty much anyone. But, I don't think it would be Wallace either because wasn't he a Republican until around 1936?