let me do what I always do (especially when trying to provoke some of the annoying die-hard fair-weather activists) and deny the influence of carbon dioxide on the rising temperature. I am open for discussions, feel free to convince me.
Do you mean the physics behind the connection between carbon dioxide and temperature? If that's the case I wrote something below.
The role of carbon dioxide (and other greenhouse gases, such as methane and water vapor) in regulating the temperature of the planet is relatively straightforward. I'll divide this into feedback 1: the direct effect of increases in CO2, and feedback 2: the indirect effect.
Feedback 1. Carbon dioxide concentration is very little by mass but has strong radiative effects. This radiative effect occurs because carbon dioxide preferentially absorbs radiation in the infrared, which is then re-emited. So, basically solar radiation, with most of the spectrum being in the visible range, gets to the ground relatively unimpeded. This heats the earth, which in turns radiates back to space, with the bulk of the radiation in the infrared*. Since carbon dioxide is efficient at absorbing at the infrared, a good portion of the energy radiated by the earth is trapped in the atmosphere, which then heats it and radiates back a portion to the earth heating it more. This is basically the greenhouse effect, and is key to human survival. Without this effect the earth temperature would be approximately 33C lower. Now, the problem is that with higher man-made CO2 concentrations this effect occurs a little bit too much than before, so the earth equilibrium temperature rises. Now, by itself, increases in CO2 would yield about a quarter of the heating that what models project for end of the century, and the rest is given by the indirect effect (feedback 2).
Feedback 2. CO2 increases give the first kick to increases in temperature. When temperature increases the amount of water vapor also increases**. Water vapor is actually a stronger greenhouse gas compared to carbon dioxide. So, taking that into account, increases in water vapor (due to increases in CO2 and other greenhouse gases) is the main driver of already observed and future increases in temperature.
*it turns out there is a temperature - peak of radiation spectrum relationship, higher temperature objects preferentially radiates at the higher energy end: visible, ultraviolet, so forth.
**close to exponentially, in what is known as the Clausius-Clapeyron relation (
Clausius–Clapeyron relation - Wikipedia). Hot places can have quite a bit more of water vapor before it condenses. Same amount of water vapor in a colder place would just form water droplets and eventually rain.