Isn't the temp supposed to go up over the next 1,000 years
see, the thing is that we don't know.
Climate science is still a relatively new field and a lot of climate science is extrapolation from incomplete data, particularly on the historical level. Since there wasn't someone measuring and recording things at all until the early Holocene, large swaths of climate science and geoscience as a whole are based on theories and predictions from data in the rock record, fossil record, etc.
We don't exactly know very much about atmospheric carbon and the correlation to global warming. For instance, atmospheric Co2 was 5 times higher during the Jurassic period, and we have no idea where it all went. It is generally accepted that it came from volcanism, but nobody can say for sure where it went. Climate science isn't "settled" (as is the phrasing I've been hearing lately), In fact it's exactly the opposite.
The entire point of science is to question everything. No science is "settled" and climate science especially so. We basically have a jumble of correlations but not many causations. I would know, I'm majoring in Geoscience.