> So the question still becomes if the temperature increased 0.5 degrees while we weren't emitting that much co2 and it's done more or less the same in more or less the same timeframe with us putting much more co2 out there. How big a part is really humans and how much is natural variation.

First of all, global average temperature increase actually has accelerated significantly since the 1950s: https://www.nasa.gov/topics/earth/features/2011-temps.html

The increase has not been proportional to the increase in C02 in the atmosphere, but that is expected. Temperature is not directly proportional to atmospheric greenhouse gasses. Rather, heat loss is dependent on them (and on other factors like surface color, which is affected by ice melting, to name one. The main one that has changed thus far though is atmospheric C02). Just because the earth is trapping more heat though, doesn't mean that the temperature will make a large change instantaneously. Instead, the change in temperature over time will be proportional to the difference between energy in from the sun, and energy out in the form of emitted heat. By increasing greenhouse gasses, we reduce the latter, causing temperature to rise over time.

Since heat emission is proportional to temperature, eventually (if we stopped emitting CO2) we would reach a new equilibrium at a higher temperature. In order to get back to a lower temperature, we need to eventually actually remove C02 from the atmosphere.

This is precisely why climate change is currently such a crisis: even if we stopped all greenhouse gas emission now, which is obviously impossible, we would still see a significant further increase in temperature due to the imbalance in heat transfer that already exists due to past emissions. The more that is added, the greater that increase will be.

Everything I've said is backed up by clear science, so if you're really looking at this with an open mind, please tell me what part you disagree with or are unsure about, and I'll be happy to provide supporting evidence.