You are focusing too much on a single measurement and ignoring exactly what is being discussed: a single degree rise in temperature merely indicates how much faster the molecules are moving in a given sample. It doesn't measure the magnitude of that energy.
For example, as I pointed out, a glass of water and the ocean. Both at the same temperature. Raise each by a single degree C. Which one contains more heat?
If you raise one gram of water 1 degree C the measurement of energy in that item was raised about 4.2 J. If you have 10 grams of water and raise that water 1 degree C you need 10 cal or 42 J. 10 times the energy content even though the temperature is the same.
The amount of energy needed to raise 1 L of water 1 degree C is a kcal or 4.2kJ. (4200 J).
The ocean contains about 1,367,290,742,000,000,000,000 liters of water. If you raise the temperature 1 degree C you have just added 5,742,621,116,400,000,000,000,000 J of energy to the ocean.
What does this mean?
Well, for 5.7x10^24J you get the following: enough energy to power the world for one year with about 10^7 J left over. More energy than the largest nuclear explosion in human history. More energy than was used by the Indian Ocean earthquake in 2004. More energy than the sun radiates. More energy than all the known fossil fuels on the planet combined.
And you say it's only a single degree?