See? It's so hard for us laypeople to understand that only the surface would get hot and there would just be a small amount of heat radiated from it, but absolutely no convection like we get on earth.
This is not actually true. The midday lunar surface radiates a lot of heat, and without proper thermal design it'll be a big problem.
Any object that isn't at absolute zero radiates light. The wavelength distribution of this light depends on temperature; the hotter the object, the shorter the peak wavelength. (A hot object first glows dull red, then orange, then yellow and finally white as its temperature increases). The sun, with a surface temperature of about 6000 K, peaks in the near IR and visible spectrum. Objects at "ordinary" temperatures, including the moon, peak in the far IR around 10 microns. Passive IR motion detectors work by your body's long wave IR radiation.
An object in space, exposed to the sun, reaches an equilibrium temperature at which it radiates just as much long wave IR ("heat") as it absorbs as short wave IR and visible light from the sun. This is the "heat balance" at the core of any model of global warming.
So the hot lunar surface emits just as much heat as it absorbs from the sun -- it's dark, so that's a lot! That's one reason we always went there in the early morning.
Real objects are not ideal "black body radiators". They do not absorb or radiate light (of any wavelength) 100% efficiently. The measure of this efficiency in the visible and near IR spectrum is the "absorbance", or alpha -- how dark the object appears to be. But it's not necessarily the same in the far infrared. That figure is the "emittance", or epsilon.
Standing on the moon it's relatively easy to shield yourself from the sun's heat: just use a low alpha (IE. light in color) surface coating. If you also want to radiate waste heat through this surface, pick a material with a high epsilon. Such a material will run cool even in sunlight.
But then you
can't use this material to shield yourself from the hot lunar surface. Why? Because radiation flows both ways. If you radiate well in the far IR, then you'll also absorb well in the far IR. It's a common misconception that thermal coatings act like "heat diodes" with alpha controlling the incoming heat and epsilon controlling the output heat. This is only true if the incoming heat is from a hot object like the sun, surrounded only by cold dark sky.
You should be seeing the problem by now. The moon is a lot cooler than the sun, so it's far less bright (if you could "see" just the moon's long wave IR, excluding reflected sunlight). But when you're standing on it the moon looks a lot bigger: 2 pi steradians, an entire hemisphere, vs only 6e-5 sr for the sun, or about 100,000 times bigger. You have to radiatively "decouple" yourself from the lunar surface by minimizing your exposure to it and/or using a low epsilon surface. (That material would also have low alpha to reject direct and reflected sunlight.)
This is exactly what the Apollo lunar suits were designed to do. They're white, so they have a low alpha and therefore absorb little solar heat. They also have multiple layers of aluminized mylar, which has a low epsilon. In a vacuum, these layers effectively form a whole bunch of thermos bottles nested like Russian dolls. The overall suit has an
exceptionally low epsilon.
So this thermally isolates the astronaut from both the sun and the lunar surface, but it creates another problem: how do you get rid of the astronaut's own metabolic waste heat? That's what the liquid cooling garment and PLSS sublimater are for. Acting together they vaporized water with the excess heat and dumped it into space. It was quite literally a high-tech swamp cooler that "sweated" for the wearer. Because it's so bulky, cooling feed water was a major limitation on the duration of an EVA.
The LM has its own thermal coatings to protect it against solar and lunar thermal radiation, and it also has its own sublimater. (Bart Sibrel seems to think it patently absurd for the LM cooling system to be powered with batteries. But it's a fact -- cooling takes relatively little energy when you don't attempt to condense and recycle your coolant after evaporating it. Bart didn't do his homework.)
The real thermal challenges on the moon were the ALSEPs left there as they had to operate over the entire lunar day, not just part of it. They couldn't expend consumables, so they drew all their power (including any heaters) from a RTG and dissipated waste heat solely by radiation.
Look at an ALSEP central station and you'll notice a rather complex set of folding mirrors. They are designed and positioned so that the radiator inside the station sees only dark sky, either directly or by reflection, never the sun or the lunar surface.
It's easy enough to avoid seeing the lunar surface: just lay the radiator flat on the ground facing up. (The ground below you will be quite cold because you're shading it.) But then sunlight can fall on it, so you need a shade that must always work as the sun moves across the sky. This took some doing since many Apollo sites are practically on the equator. The shade must also avoid radiating its own heat onto the radiator, and the easiest way to do that is to cover the shady side with a mirror (most shiny metals have very low epsilon). But don't let the mirror reflect the lunar surface onto the radiator! When you're done you'll have a system of mirrors that "show" the radiator dark sky at all times.
So the bottom line is that the lunar surface
is a significant source of heat that must be dealt with through careful thermal design. The behavior of heat on the moon is probably its weirdest and least intuitive physical phenomenon, and that's saying a lot, but the physics has long been well understood and routinely applied by spacecraft thermal engineers.