no but in a vacuum it certainly would.

Ah, maybe so. In my defence, I've not spent much time in vacuums. I am having difficulty picturing it though... if more energy is initially reflected away from the surface, then won't there be less energy available to actually heat the body? - and therefore it'll be able to reach equilibrium at a lower temperature? (I presume radiated energy loss is proportional to body temperature) ... Unless the increase in radiance due to the surface colour exactly (inversely) matches the effect of the initial reflectance...

   - Andy.

no but in a vacuum it certainly would.

Ah, maybe so. In my defence, I've not spent much time in vacuums. I am having difficulty picturing it though... if more energy is initially reflected away from the surface, then won't there be less energy available to actually heat the body? - and therefore it'll be able to reach equilibrium at a lower temperature? (I presume radiated energy loss is proportional to body temperature) ... Unless the increase in radiance due to the surface colour exactly (inversely) matches the effect of the initial reflectance...

   - Andy.

Well heat loss goes as the 4th power of absolute temp, and yes, absorption and emissivity are exactly equal for very good reasons of not breaking the laws of thermodynamics.

Edit

Let us investigate where that simple equilibrium would be with 1380 watts/m2 incident would get us- if the simple model in the original post really applied.

First we need the constant relating power and temperature, so thanks to messrs Stefan & Bolzman, this  is measured as

5.670374419 × 10⁻⁸ watt per square metre per kelvin to the fourth

So to radiate off that 1370 watts arriving per square metre needs  a temperature T such that

T= 4th root of (1380/5.67E-8) = 4th root of 24338624338 = 395K

or ~ 121 degrees C

Really that simple sum should have been attached to the  original dialogue, as it makes the point rather well that the simple model that  illumination and radiation are in equilibrium and it can be assumed to be perfectly uniform is imperfect.

It certainly gets you close enough for a first go, and  121 C is well within an order of magnitude of the right answer,  (a full order  of magnitude would permit anything between 30K to 3000K ) but is not an accurate enough model to get close enough to explain why we are not all dead ;-)
Luckily the system is rather more complex than the simple view suggests. It helps that the emissivity of the planet is not uniform, so it does cool off rather more at night than it absorbs during the day , when working properly.

Mike

PS it is quite fun to halve the incident solar power - perhaps the planet cools for 24 hrs per day but warms for only 12. Then 690 watts per m2 illumination.

T= 4th root of (690/5.67E-8) = 4th root of 12154306852 = 333K

or ~ 60 degrees C again close, closer actually, but not right.

The effect of halving the solar input is a 60 degree fall in equilibrium temperature - the effect of that 4th power is that you need surprisingly large changes in solar flux to alter the temperature very much at all.

Again, all we have learnt is that this simple model is not the full story.

https://www.tec-science.com/thermodynamics/temperature/stefan-boltzmann-law/

Interesting.