I never said heat couldn't radiate into a vacuum.What I did say is that that process alone could not shed the heat produced by the equipment, the astonauts themselves and the effects of solar energy being absorbed by the spacecraft. Remember, we are talking about a wide spectrum of energy coming from the Sun, reflective material is not sufficient to prevent heating.
While the outer skin of the vehicles may have been 'really shiny' and the insulation very good between this "skin" and the inside, there is no escaping that a buildup of heat energy would occur that some process would be required to mitigate.

Jay has described in a fairly detailed explaination of the cooling process that was used on one of the spacecraft components and a bit on the other. I need to review carefully the information and compare it with my own ebfore I comment.
I would also request he source his information, if possible, so a detailed review of it can be made. One thing that has never been explained to me as of yet is why A13 would be cold when we all see a cooling apparatus was required during normal operation. How much heat did the electrical circuits that were lost or deactivated contribute to the overall heat budget of the spacecraft? Why would there be excessive heat from properly wired and installed electronics? I know there would be a very minimal amount of heat produced, but it seems irrelevant in the overall heat budget.
What we need to determine is approximately how much heat was being produced internally and how much was being absorbed from the Sun, and determine what temperature the vehicle would have to get to before it reached equilibrium, that is loss of heat through radiative forcing+other processes Jay mentioned=Heat produced internally by the spacecraft and absorbed from the Sun.
It is my contention that an object in space this near the Sun nomatter how well insulated internally will eventually heat up to an very uncomfortable level, and it has basically only one way to shed heat. Jay claims another, radiators.
In my experience radiators work by circulating a coolant such as propylene glycol anti freeze mixed with water through the object to be cooled, and then through a radiator, which removes heat from the coolant when air passes over it. Though it is called a radiator, radiative forcing represents only a small amount of the heat actucally removed. Thats why your car has a fan on the radiator. Now I understand this is a very special radiatorJjay is refering to, and I am looking into it now.