Yes, CO2 does increase the heat capacity of the atmosphere. Yes, industrial processes release CO2.
HOWEVER, if that was all there was to it, the global temperature increase would pretty small. (Probably measurable over a long enough period, but not enough to have a serious impact.) It is the supposed secondary effects that are claimed to produce the large changes. e.g. A slight increase in temperature increases the water evaporation rate faster than it increases the rainfall rate, so leads to an increase in cloud cover, and clouds trap heat, so the temperature goes up further. To model this sort of thing accurately you need a very good model, otherwise you get answers that are probably wrong, although also possibly just what your assumptions lead you to think it should. Early climate models did not even include clouds, and the above chain reaction was used outside the model as an 'obvious' argument for global warming. I have not looked at the current state of models for some time, but even after some started to incorporate cloud modelling they still did not include atmospheric dust. Higher temperatures lead to more ground dust, which is picked up by the wind and becomes nucleation centres for rain drops to form on, reducing the cloud cover again, counteracting the above change.
Why do you think that the models have not predicted the pause in the temperature rise for most of the last two decades, where explanations such as deep ocean heat absorption are now been suggested? It is because the models are incomplete, and so provide forecasts that may sometimes coincide with reality and sometimes diverge.
My background is as a physicist, and I used to produce computer models. Just simple ones of a dozen electrons, but changing a few parameters slightly could lead to large changes of behaviour. When somebody says that drastic action needs to be taken I need more assurance than 'The computer model says so.'