They are very much ad hoc. At worst they could be considered glorified curve-fitting solutions with a large number of free parameters, like epicycles. At best they are an incredibly incomplete and flawed way to model the global climate.

Consider, many very fundamental aspects of climate modeling are typically just approximated using an empirically derived "fudge factor". For example, the interaction between the ocean and the atmosphere and the transfer of heat between them, that's not derived from an extensive analysis from first principles, it's typically merely parameterized. The same goes for clouds which have poorly understood effects in climate science (combining both cooling and insulating aspects). And it's even true for the impact of CO2 concentrations as well.

The idea that we have a robust, from first principles understanding of climate science is patently ridiculous. Now, that doesn't discount the possibility that we understand climate well enough to make strong, well founded predictions about it. We should always be extremely careful to understand the limitations and assumptions of our models, because failing to do so is a recipe for being surprised when the real world deviates with your imperfect simulation of it.