The system is massively complex and anything can happen including a lag. But being that they know the Earths climate exactly, it will be simple. Put your money where your mouth is... and if you are wrong...
I’d want to see more effort put into determining the “heat level” of the globe. As it is, we have temperatures taken at or near surface level. And without reference to enthalpy (moist air? dry air?) That can hide a lot of features.