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It's not my model, it's the models that predict temperature increases based on CO2 increases. The only way a model can do that is to accurately model many inputs and many functions (not sure what you mean by transfer function). Some of the inputs matter a lot like solar input, atmospheric gases including forcings such as increasing CO2, topography, etc. Other inputs don't really matter as much like current weather (initial conditions for the weather part of the model). Then the model has to calculate subsequent conditions for a sufficient resolution grid at a sufficiently small interval of time for the length of time desired.

What resolutions are needed? Current resolutions are woefully inadequate, typically 100 km horizontal, 25 vertical layers, and 10 minute intervals. The last one, time interval may be ok, but the grid resolution clearly sucks since climate affecting weather is mesoscale 10km and sometimes small scale (1km) in the case of tropical shower activity. The essential problem is that small scale weather activities like the tropical showers pump water vapor up into the upper atmosphere where it causes the most amount of greenhouse warming. If they are not modeled accurately, then the climate prediction results will be wrong.

My point in bringing up the models was that once computer power is sufficient for adequate models, they will be useful to calculate the effects of simple and cheap climate countermeasures that might be needed. The current Kyoto countermeasure is estimated to cost about $100 billion for each 1/1000th of a degree of hypothetical cooling, an outrageous amount of money for a completely inconsequential result.