The CO2 level has increased by 50% since preindustrial times. You don't need a super-complicated model to figure out what that does to the global average temperature. It was predicted with decent accuracy in 1896, based on simple thermodynamics, and better accuracy several decades later with just slightly more complicated physics. No fancy computer modeling at all, just a calculation that a physicist can work out on paper, and we've been right on target since then.
For details see the recent little book The Physics of Climate Change.