I know that the comment is sarcastic but just in case, this will have the opposite effect, yes nuclear bombs will produce a lot of heat but that is for short amount of time and fires it will produce will last for sometime. But on the long time scale (months to years) the particles will precipitate in the sky and trapped and will cover most of the planet by radiation clouds which will prevent most of the sun photons from reaching the earth. So goodbye for planets and it will be the worst winter in earth's lifetime.

Then you say small? But how can we have small nuclear war? The effects of any nuclear exchange will be seen throughout the world (not in geopolitical sense).