When it comes to having a conventional World War Three, it's usually in the 80's, of which I find a bit overrated, though granted at the time NATO's military is at least on par with the Warsaw Pact's and that the USSR was on the decline by the end of the decade. In the 60's however (to my knowledge at least), the WP's military is somewhat stronger than NATO's and that France's withdrawal from NATO in the late 60's complicated the situation (along with the USA being focused on the Vietnam War), not to mention the whole nuclear strategy of massive retaliation in place until the late 60's by the USA (and the USSR's hybrid nuclear warfare thing). Still, I feel like the 1960's is an interesting time to have a war play out (not counting the Cuban Missile Crisis), namely that some of the hardware made in the decade were and still are in use afterwards and as some other thread pointed out, there were multiple flashpoints were things could have been escalated out of control. So your challenge is with a POD after 1946, have a Third World War occur yet happen as a conventional conflict (at least initially). Bonus points if it doesn't involve the OTL Cuban Missile Crisis given the importance of the USA's Massive Retaliation strategy.