Hitler Greatest German Hero
In the TV documentary "The Seduction of Adolf Hitler", a former Hitler Youth member and historian noted that if Hitler had died in 1940, before the Holocaust, he would be considered the greatest German leader since Bismarck. I have heard several different voices from other sources echoing this thought.
Hitler's death at this time makes him a hero with the German people since by this time France is being humbled. Indeed Hitler's mystique by his death at this time would be boosted in the same way that President Franklin D. Roosevelt's was since Roosevelt died just short of victory. In the same way Hitler dies just short of seeing the French, hereditary enemy of Germany, humbled.
My humble guess is that a triumvirate forms to lead the Reich led by Hess, Goering, and Himmler. It is Goering and not Hitler that gets to gloat at Compeign and receive the French surrender. Given Goering's arrogance I would also say the Battle of Britain also occurs pretty much as it did in OTL.
Hess does not make his famous flight to England. Rather he tries to persuade the other two in the triumvirate that it is to their best interests to negotiate with Britain while preparing for the war with Russia. This may delay but not stop Barbarossa by several months to a year, allowing the generals to develop slightly better plans.
Barbarossa kicks off in 1942 rather then 1941 due to Hess's insistence on attempting to get a separate peace with Britain. Both Germany and Russia are better prepared for the war. Whether Germany still aids Mussolini in his bungled attempts to take Greece and in North Africa is up in the air. None of the triumvirate would have felt particularly disposed to aid Mussolini on the other hand leaving the Balkan front exposed would not be acceptable. I leave these areas of consideration for others on this thread to consider.
In any case, I see the war lasting longer and possibly ending more along the lines of Calbear's scenario in the Anglo/Nazi war TL. There is one major difference, it is Himmler, Goering, and their "gang" that get the blame for the holocaust. As far as the German people will be concerned, Hitler remains an untarnished hero (shudder!!

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And THAT is a truly frightening prospect!
Geon