The 2nd law of thermodynamics :-)
If the sun is at 6,000K, it's not going to be able to heat a planet up to 10,000K in a sustained way - otherwise energy would be flowing from low temperature to high temperature, which can't be done without expending "free energy" (a technical term in thermodynamics, which basically means useful energy that you can get work out of) somewhere else - otherwise you violate the 2nd law. For example, an air conditioner only works because there's a power plant somewhere that's burning coal, which has a lot of free energy stored in it which is released by the burning and used by the power plant.
In reality, it won't even get the planet up to 6,000K. The way the greenhouse effect works is that a body has a different albedo (how efficiently it both radiates and absorbs energy - they have to be the same) at different wavelengths. Lower temperature bodies want to radiate at longer wavelengths - think of orange coals vs. white flame in a fireplace. So if you have a body which neither absorbs nor radiates at long wavelengths (low temperatures) but absorbs and radiates well at short wavelengths (high temperatures) and shine high-temperature light on it (from the sun) it will heat up more than one that has a uniform albedo. Basically it needs to heat up more in order to radiate the absorbed energy away. But if the threshold for change in albedo is too high, it won't absorb any energy in the first place, so the effect is cut off.
John
That's not the way this works at all. The sun is constantly expending atomic energy to produce all that heat. In turn the very hot and dense hydrogen at the surface of the sun has to get rid of that heat somehow or else it would be much hotter. Heat doesn't travel through a vacuum but light does so the light from this hot gas leaves the Sun. The energy from the Sun going to some planetoid doesn't have anything to do with how how the target is.
Instead we have two things on the target that control the temperature. We know that a thing is white if it reflects a lot of light (and there is roughly white light pointed at it,) and that is the albedo. If the light isn't reflected it is absorbed, and just like physically hitting an object that makes it heat up a tad. In turn for the planet to give off heat it also does this as light- but different wavelengths. Hotter things give off shorter wavelengths of light.
After that greenhouse gases are like a hot car in the Summer. Visible light goes in through your windshield and if it is reflected it goes right back out. If it is absorbed it heats the seats and things up and then later they eject some of their heat as light, mostly infrared. If you're talking about infrared light glass and greenhouse gases aren't transparent at all- they're more like a solid lightish gray for that section of the spectrum.
So this gives us a really different answer for why greenhouse gases can't heat up a planet more than the star the light is coming from: if the gases are catching 100% of the infrared (or whatever range of colors it catches) then the planet will heat up until it gives off colors of light they don't catch.
*and if they stop all colors of light they're anti-greenhouse gases because the light can't get in in the first place.
**and the planet can only have 50% of it's surface pointing at the star to catch light while 100% of it can be giving off light as it cools- though the light it gets from a star is even less that 50% of the area. Instead the equivalent area of light it gets is the cross section of the planet.
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I don't think the equations in game really reflect this real world function but the upper limit is most likely a shortcut for getting a similar effect.
*You can also lose atoms from your atmosphere and heat with them. On geologically active worlds there is usually a magnetosphere to keeps the solar wind from making ions out of your water vapor and such but the game doesn't seem to touch on this at all.
Uhm, not the point I meant to make.
Starting over (not entirely) at basically every temperature hot (as in not super-cold) material gives off at least a little short wavelength light. You hit a point where you're giving off lots of light that will get past greenhouse gases well before you're actually giving off mainly visible light (meaning when the ground would be "red hot. ")
Look up black body radiation if you want to know more about what light things give off.
My (somewhat tongue-in-cheek) answer was that there are 2nd law reasons why one can't just wave the magic "greenhouse effect" wand and obtain arbitrarily high temperatures. To put it a different way, if you put a black-body marble in the center of a 1,000 degree (black-body) oven, it will eventually heat up to 1,000 degrees, but it won't get hotter than that (assuming you don't have a source of free energy somewhere that you're using to run a heat pump) - this is Clausius' statement. Putting greenhouse gasses around the marble isn't going to change that. And if you cut away 99% of the solid angle of the oven (so that the bit that's left is analogous to the surface of the sun that's emitting at us), you still aren't going to make the marble hotter than 1,000 degrees. This isn't to say that it's impossible to make the marble hotter than the oven remnant - once you've cut the 99% away it's implied you've got a source of free energy (otherwise the oven remnant would radiate away all its heat and drop in temperature), so you can play all sorts of games like your mirror or lenses to make it hotter. It's just saying that the greenhouse effect alone isn't going to do it for you.
