I think he'd at least by sympathetic to the New Deal, after all it was modelled after his Square Deal, but whether he'd vote for FDR would depend on familiar tensions.
There weren't any between Franklin and TR. TR ADORED him and said to him once that if he could have had one wish it's that "you would've been a Republican".
Yeah, the one who hated FDR was TR's daughter, Alice Roosevelt Longworth, who was a fascinating and idiosyncratic woman not all of whose views reflected her father's.
Don’t forget his ultra-right-wing son Archibald.
Didn't Teddy Jr. want to quit his ambassadorship or whatever specifically to return to the US and campaign against Franklin? (EDIT: I reread his Wikipedia page--it was while Governor of the Philippines; for the record, TR Jr.'s previous service as Governor of Puerto Rico, and his subsequent role as a general in WWII seem to indicate some very admirable traits)
