In a nuclear explosion, most of the energy of the bomb is released as pure heat, the nuclear tests of the 1950s and beyond were all carried out in deserts and in the atmosphere where nothing flammable really exists. If you "nuke" a large city with a modern nuclear weapon, a city full of materials, chemicals, plastics, woods, factories, etc - it releases a colossal amount of debris into the atmosphere. If you do this to many cities at once the result is that so much stuff ends up in the atmosphere, the temperature of the planet - the whole northern hemisphere drops.
The temperature in the northern hemisphere drops 10-20 degrees in the first 6-12 months, due to the smoke in the atmosphere.
All crops fail due to temperature/poor sunlight and can't be re-grown, no food. (this is happening to most of the planet)
The atmosphere is full of radioactive dust, water is poisoned and remains poisoned for a long time.
Due to reliance on food-aid, nearly all 3rd world countries perish, due to America having no crops to provide aid.
Basically the effect on the climate, of unleashing that many nuclear weapons upon that many cities in one go - wouldn't be that far off an extinction level event, billions die, nobody needs to retaliate - and this is why in the 1980s, the scientific community including Russian and American scientists all agreed, that a pre-emptive strike is suicide, even if the other side doesn't get a single warhead away.