Their strong case is that CO2 is a greenhouse gas, which was not in contention.
The Climate sensitivity (ECS)of the added CO2 is what is in question.
The IPCC started with the range of 1.5 to 4.5 C,
http://www.grida.no/climate/ipcc_tar/wg1/pdf/tar-01.pdf
IPCC AR4 changed the range to 2 C to 4.5 C,
and IPCC AR5 went back down to 1.5 to 4.5 C.
The observable data points to an ECS of between 1.8 and 2 C for a doubling of the CO2 level.
At the current rates CO2 could double by about 2070,
this assumption is based on an ever expanding access to inexpensive oil, which does not seem likely.
We have already located and exploited the cheap, easy oil, what remains is neither cheap or easy.
Fracking is evidence of the supply being limited. The fracking produced an oversupply,
which if anything, demonstrated the poor risk reward of fracking oil wells.
It increases the flow, at the expense of well life.
Oil has a very finite future, of roughly $100 a barrel, and few investors will risk capital
if that is the limit of the return.