The cockroaches.
Not yet, there's no H-Bombs and only the US has the bomb.
The Soviets make initial progress due to superior numbers but US/UK air power and supply line problems stop them before they can get to the Channel or the Pyrenees. Atomic weapons are used against Soviet troop concentrations and unfortunately a lot of Western soldiers will be exposed to radiation along the way as they march through the gaps in Soviet lines.
Over the next two years the USSR is slooowly pushed back and its newly acquired satellites revolt. This goes on until either a peace deal is made with the Soviets basically back to 1939ish borders and their influence in Eastern Europe gone, or the USSR straight-up collapses and the "UN" (but mostly the US) ends up occupying a chaotic former USSR. This probably causes all sorts of resentment and problems later on, but maybe the US will be able to rebuild Russia et al. the way Germany and Japan were rebuilt. I doubt it though.
If the Communist Chinese leadership is smart they will quietly take over Nationalist China while the world is distracted, but not get involved in the war.
Alternatively someone in the Politburo sees the writing on the wall early on, puts together a coup and tries to make peace with the West on the best terms possible. Given the cost of WWIII the West is probably good with this.
However it turns out there's probably even more accelerated decolonization as Western Europe is even more blown up and bankrupt, and probably a lot of pacifist sentiment around the world. I mean, a third world war just 3 years after the second? It's horrifying.