Weather forecasting (meteorology) is not climate modelling. As such, a meteorological model to forecast temperatures over years is not the right tool for the job.
But there is indeed a very, very simple climate "model" that only accounts for CO2 and temperature.
You find it here:
https://scied.ucar.edu/simple-climate-model
with a little guide:
https://scied.ucar.edu/activity/very-very-simple-climate-model-activity
and more info here:
https://www.windows2universe.org/?page=/teacher_resources/teach_climatemodel.html
The question was "simple", and this is simple. It only shows a single dependency but may be useful to demonstrate a relationship. Of course "real" quantitative modelling depends on ridiculously much more and is constantly improved and updated.
