1 Megaton TNT is apparently 4,500,000,000,000,000 Joules (4.5 x 10^15)
So 5,025,000,000,000,000,000,000 Joules would be
50,250,000 / 4.5 = 11,166,667 Megatonn
About eleven million megatonn per degree celcius for your air.
What is so special about that amount of air? Is that the whole atmosphere?
Whatever it is, do not panic. The amount of danger from energy depends greatly on the structure and other properties of the system. It may be deadly when diffuse or it may be deadly when concentrated.
You can burn you finger with the match - at worst you will get a nasty burn that will bother you for a few weeks.
If you apply exactly the same amount of energy to your finger as ionising radiation - gamma, alpha, neutrons - you will get pretty much the same burn that will heal in comparable time.
But if you get the same amount of radiation evenly over your whole body, you will be dead in days or hours.
Our organism deals much better with localised damage/death to the tissue then system-wide spread of tioxic radicals.
On the other hand, the whole athmosphere may be able to store some extra energy with no noticeabole effects or even with greater stability.
With increase in 2 degrees, the cloud cover would increase too. Besides having stabilising effect on temperature, it may actually reduce irregularity in energy absorbtion (by ground/ocean) and the weather could become less violent, not more!
Local violence should concern you more then global effects when the weather is concerned - you are likely to be hurt by a thunderbolt or a flying cow rather then general increase of temperature by 2 degrees.
Of course lack of sun causes significant increase in suicides, but those are most likely to be unstable individuals.
As more water vapor makes its way up into the athmosphere, it will be more actively split into oxygen and hydrogen by cosmic radiation, with heavy oxygen staying down and light energetic hydrogen partially escaping into space. So the sea levels will go down! Granted, the process is not that fast, but apparently the Earth have already lost equivalent of about 6 meters (20 feet) of water over the whole surface.
miko