A Different Cold War

Let’s say Hitler had defeated Russia and invaded England, along with total control of Europe.
I just wonder after the U.S.A finally defeats Japan, would a cold war situation had risen or America kept to herself?

 

I would believe that the US would certainly not remain isolationist anymore, especially seeing their democratic counterparts in Europe being swallowed by Hitler(and doing nothing) and the problem of previously Japanese occupied colonies in Asia.

Europe to Nazi Germany and America and Asia to US.

The question is whether the huge British colonies (like India) not captured by the Japanese will then be whose ?