A win of Barbarossa would have resulted in a redoubled hot war on the Axis’ western flank since that meant the eastern front was secured. Neither Hitler nor Churchill (already at war for two years prior) would have sued for peace in such an eventuality. Wins emboldened Hitler rather than made him settle for any sort of “cold war” situation.
The Allies were in fact convinced that Nazi Germany could have achieved atomic breakout before the war actually ended, particularly due to the fact that it was in 1938 that German scientists discovered how to induce nuclear fission (hence missions like Operation Big). Should Hitler have secured the whole continent, he would have had the time to produce atomic weapons far more rapidly, and he would have used them.
In Mein Kampf Hitler conceded the the British Empire was no threat to the Reich in the sense the part of the world controlled by British imperialism were not on the Reich's radar.