The "Ice Age" theory came from two things: 1) changes in the Earth's orbit 2) the cooling effect from smog aerosols. If it wasn't for our extra CO2 we could've seen some cooling but we keep on blasting it up there so...yeah.
As for less atmospheric C02 than expected, that's because the oceans have been absorbing most of it (as well as a lot of the heat). The oceans won't be able to absorb forever though.
As for the "production gap", before humans were on the planet the Earth's climate changed due to fluctuations in energy from the sun (mainly from orbital variations) as well as volcanic eruptions. Focusing on the fluctuations from the sun, yes, temperature would rise a bit first, warming the oceans. As the oceans warmed they would release more of their carbon dioxide starting a feed back loop to even more warming. CO2 in the atmosphere does cause warming, otherwise we'd be as cold as the moon.