There will not be WWIII IMHO..... wars are now fought from a distance with smaller land based troops and through economic and political sanctions. Putin will believe he made his point and withdraw and then try to undermine the government. I think he is still smart enough to know no one wins an all out war.
It'll just be a cold war conflict like AFG/Korea/Vietnam/ etc... We'll kill Russians and Vlad will accept the American plausible deniability to avoid declaring war.