According to NASA, earth's atmosphere weighs 5.1e+18 kg (comes to ~5,600 trillion US tons).
According to The Engineering Toolbox, it takes 1006 Joules (of energy) to change the temperature of one kilogram of air by one degree Celsius (or Kelvin).*
1006 Joules/kg/°C per 5.1e+18 kg comes to 5.712e+21 Joules to raise the temperature of earth's atmosphere by a single °C (or °K).
5.712e+21 Joules converts to 1.425 trillion Mega-Watt hours.
The largest nukular reactor in the US (in Palo Verde, Ariz.) can produce 3937 Mega-Watts if all three reactors are running @100%.
Running @100% 24/7/365, in a year's time, Palo Verde would make 34,488,120 MWh.
Running at 34,488,120 MWh per year, Palo Verde would need 41,323 years to produce the 1.425 trillion MWh needed to raise the temp of earth's atmosphere by one degree C (1.8 °F).
Or to put it in another perspective, the Global Cooling Scare began about 1970. If we had brought enough reactors online that year in a deliberate effort to raise earth's atmosphere's temperature by 1°C (or 1°K, or 1.8°F) by running them @100% 24/7/365 until today, and converted ALL of that electrical output into heat, we would have had to build 780 Palo Verde-sized reactors (assumes 100% efficiency in the conversion).
Today there are only (roughly) 220 commercial nuclear power plants on the planet.
To put that in Imperial measurements (1°C = 1.8°F), Palo Verde would need 22,957 years to make enough MWh that if converted 100% to atmospheric heat could raise earth's temperature by 1°F.
Or if we had started in 1970, it would have taken 434 Palo Verde-sized reactors to raise earth's temperature by 1°F by 2023.
This obviously is an unfathomably YUGE amount of energy, far in excess of what a gas that comprises a whopping 0.04% of our atmosphere could be responsible for.
* Yes, I am aware this specific heat value only applies to air @sea level pressure but the scale of final answer is so absurd that I couldn't be bothered to find a mean value.