...conduction through the cylinder walls, cylinder heads, etc. weren't mentioned because they don't change when you take out your thermostat. The only thing that changes is the convection heat transfer between the liquid stuff (coolant) and metal stuff (engine block, heads, radiator, etc.). Barring any oddities like boiling in the engine or pump cavitation, the heat transfer between the coolant and metal will increase when you increase the coolant flow rate by removing the thermostat. This means that the coolant will be sucking more heat from the engine parts (block, heads) and delivering more heat to the radiator metal. If the amount of additional heat sucked from the engine metal is more than the amount of additional heat being delivered to the radiator metal, then the steady state coolant temperature will rise. If the opposite is true, then the steady state coolant temperature will go down. It's really that simple.
With all of the sucking and delivering above, there must be an R-rated joke somewhere...
@bryesh: In the radiator, there are three heat-transfers that occur - convection from the coolant to the radiator metal, conduction through the radiator metal, and convection from the radiator metal to the air. By far, the convection from the radiator metal to the air is the highest "resistance" to heat transfer. To give you a number, the heat transfer coefficient between the coolant and metal is about 6 to 20 times the coefficient between the air and metal. Let's say you have a big-ass radiator with a big-ass fan, and your air-to-metal heat-transfer coefficient is pretty good (closer to 1/6th the coolant-to-metal coefficient). Then, increasing the heat transfer coefficient on the coolant side will help the radiator reject a meaningfully higher amount of heat. Now, let's say you have a small radiator, little fan, and a FMIC blocking the air flow - your air-to-metal heat transfer coefficient is pretty poor (closer to 1/20th the coolant-to-metal coefficient). Then, increasing the coolant-to-metal coefficient won't do nearly as much for the overall heat transfer out of the radiator - the resistance to heat transfer on the air side is just too dominant. Like you said, if the air-to-metal heat transfer in the radiator is low enough, then you can pump all the coolant you want, but the increasing coolant-to-metal heat transfer coefficient won't help the radiator reject more heat to the air. (BTW, since that higher coolant flow rate is also sucking more heat out of the engine, this is the most likely case where steady-state coolant temperature will increase). Clear as mud?
Mike