I contacted my friend Matt Haugland at the University of Oklahoma about his views on climate models. He has a Ph.D. in Meteorology and owns several weather related companies. With permission I quote what he said about climate models.

They're basically simple versions of regular numerical weather
prediction models that solve a set of equations based on physics. Unlike
weather models, they cover a much longer time period and include
projected changes in greenhouse gases.

It's very easy to determine how a change in greenhouse gases would
impact the global temperature if all other factors are equal. What makes
it difficult is that the other factors are not equal and are dependent
on each other and cause positive and negative feedbacks. For example, an
increase in CO2 would increase the temperature but would also increase
plant growth, which would act to reduce the temperature, but would also
add more water vapor to the atmosphere, which can increase the
temperature, but can also create clouds which would reduce the
temperature and create precipitation, which would increase vegetation,
which would reduce the temperature, etc. etc. The way these things
interact is extremely complicated and nearly impossible to predict well,
even with the best climate models. And of course, a lot of assumptions
are made, which may or may not be accurate.

We can say for sure that the earth's temperature has been increasing.
But I don't think anyone knows for sure how much of that is because of
fossil fuels, etc. and how much is because of urbanization, agriculture,
ice caps melting (which has been going on for many thousands of years),
deforestation, changes in the sun, other natural cycles, etc. And
unfortunately, climate models are either not good at or completely
unable to represent such factors.

By the way, I believe the best (or at least one of the best) climate
model is run right there in Boulder at NCAR's Mesa Lab.