My 1990 Mazda 626 leaks oil like a sieve, so I regularly top up the oil.
In a moment of stupidity, I opened my radiator cap instead of my oil cap while topping up my engine oil, and poured about 50-100 mls of engine oil into my radiator.
What implications is this likely to have on the car?
Normally, I would ask first in a comment but that seems to be a privilege not available to new users, so here goes:
Are you sure it was the radiator cap and not the overflow bottle? The radiator is usually full and getting 100ml in would be a struggle, not to mention that the green coolant would be staring you in the face. If you radiator wasn't full then you either have an empty overflow bottle, or your system wasn't burped properly the last time the coolant was changed, or you have a leaking head gasket introducing combustion gasses into your coolant system.
If it was the overflow bottle, there's a good chance that you car hasn't drawn the oil in from the overflow bottle yet. I say this because the pickup for the overflow bottle is near the bottom of the tank, engine oil floats on water and is insoluble in water.
My advice then is to remove the overflow bottle, clean it with a degreaser and refill with coolant. If you did actually get it in the radiator, let me know and I'll edit this answer.
As far as implications of oil in the radiator go: Oil will, in theory, attack the hoses and water pump seals. This would probably be a long term degradation rather than a sudden failure, and given the oil problem I doubt your engine will survive long enough to see the long term effects. My father's vehicle has been running with a slight oil-to-coolant leak for about two years, without any (visible) ill effects. The vast majority of the oil (after you've removed the head of oil floating in the radiator filler) will collect under the radiator cap as a creamy goo, which you can periodically remove.
Replacing the coolant wont do much to remove the oil that has coated the inner surfaces of your cooling system. If you have oil in the radiator and haven't run the car yet, siphon out the oil before it touches any more surfaces in the cooling system.
You need to drain the coolant and replace it.
You should follow the instructions in your owners manual. If you don't have one handy, the ehow page is a fairly general set of instructions but it'll get you into the right general location for the coolant drain.
Keep in mind, engine coolant is toxic and should be disposed of properly. This is a perfectly reasonable time to consider having a professional flush the coolant system for you: they will dispose of the coolant properly, allowing you to avoid the hassle.
Oil in the coolant won't kill the car. It's something that can happen with a bad head gasket. However, it is definitely not a desirable state.
You should flush the contaminated antifreeze out. Additionally, use of a surfactant will help clean out some of the residual oil.
The residual oil doesn't appreciably impact thermal transfer, but it may have an adverse effect on hoses. It will not hurt the bearings or seals in the pump, at least for any of the pump seals I have seen.
It's not necessary to use a flush, but for a surfactant, I would suggest about 1/2 oz of Dawn dishwashing liquid. Run that in the cooling system for about 20 minutes after the engine reaches temperature. Then flush with water, again running the engine to full temp and then for 20 minutes. Likely a total of three flushes will be necessary, depending upon how completely your system drains. Pulling a lower hose can sometimes speed the drain, and may get more of the old fluid out.
The oil will not impact the operation of the thermostat. The biggest impact is on hoses, in that it may accelerate degradation. Your mileage may vary, as some hoses are very resistant to oil, and some are less so.
