The thing about 1 average degree is that the warming isn't 1 degree across the board. The tropics aren't going to really be affected that much, so it turns in to a few degrees further to the north or south, and that's a big difference in a colder climate.
There's a lot of data out there. A lot of it is from ice cores that have air bubbles in them. They can measure the CO2 content in the air and estimate the temperature at a point in time (based on how deep the core is).
The data kind of looks like a sine wave, with the temperature having peaks and troughs over a long period of time, but there are smaller waves on the big wave, and smaller waves on the smaller waves as there are 10,000 year cylces, 1000 year cycles, 100 year cycles, etc when it comes to the Earth's average temperature.
A lot of people seem to disregard that the Earth has been a lot warmer in the past than it is now. I don't doubt that people have had a effect on global warming, but it's really stupid to think that we can actually make a huge impact on the global warming issue.