> "a few degrees, what difference does that make?"
Maybe this helps: Think about when we have a fever of "a few degrees", say, instead of 37 degree Celsius, we have 40. It shows that also a few degrees can make a huge difference.
The temperature of a fever is not measuring the temperature outside.
Think even bigger. 1 degrees inside your house? Not noticeable at all. But on a planet-wide scale? A 1 degree difference requires a LOT of energy.
It's like boiling a cup of water vs an Olympic sized swimming pool. The latter is going to take a lot more energy than the former.