Let me see if I can set the conditions more exactly.
You’re in a 10-foot cube. Atmosphere, humidity and pressure maintained at Earth surface conditions. One face of the cube always faces the Sun, constructed in some way to absorb all the solar radiation and turn it into heat. Other faces perfect insulators: no energy in or out.
Taking into account the heat generated by your own body, what is the farthest distance this cube could be from the Sun that is able to maintain this at 70F (i.e., passive heating)?
So the solar side only absorbs, doesn’t radiate? And no other sides radiate? Then internal body heat will rise till you gurgle and melt. You might not reach the stage where you pop. Try forcing HOT liquid into an escape-proof jar. Hot enough –> it melts. Forceful enough –> it explodes.
No safe distance exists for that setup. Now, if each edge of your cube sprouted a 10-foot-square radiation fin, survival may be possible somewhere out there.
True trivia: The first successful treatment for syphilis was… malaria! Which induced a high fever! Which cooked the clappy bacteria! Your space cube could be as effective. Moral: *Something about sex in space. *
I second the “you die” response above. That’s kind of what I was getting at with my spacesuit example upthread. The only thing that kept me from definitively saying that you’d end up passing out and dying from heatstroke in that example was the knowledge that there would be some vector for heat loss (I’m just not sure how it would compare over the surface area of a suit to what you could get from the sun at any given distance, but your theoretical example has eliminated that complication).
The functions of your body and the sun both are sources of heat input, and you’ve eliminated any potential for heat loss with your perfect insulator, so the answer is the temperature just keeps going up, though not quite as fast once your body shuts down and dies and you at least lose that source of heat input. (Unless the one face that absorbs heat from the sun can be allowed to bleed heat out through thermal radiation as well, in which case the question posed is similar to my spacesuit problem: what exactly is the rate at which your—until now strictly theoretical material—is supposed to be allowed to radiate heat out? Because then it’s a question of at what point the rate of heat loss through that one face, which should in turn be a function of the temperature of its surface and inside the cube—the system overall—will equal the rate of heat gain and reach an equilibrium.)
So…
Perhaps a better setup would be, say you’re in a cube that maintains a steady 70F through… some mechanism, along with a breathable atmosphere at standard atmospheric pressure with negligible humidity and negligible effect from forced air flow. At what distance from the sun would you still be able to detect the sun’s light on your skin? Like, if someone blindfolded you and spun you around, how far away from the sun could you be and still detect it through the photosensitivity of your skin, literally “feel the warmth of the sun”?
If you put a block of metal (which conducts well enough to make its internal temperature pretty uniform) in orbit around the sun, and give it just the right spin that its same side always faces the sun, you could pick whatever temperature you wish over quite a wide range including comfortable living temperature, and achieve it through a combination of what shape you give the metal, and which surfaces you paint black and which surfaces you just polish.
One relevant distance in this discussion could be the so-called ‘current snow line’, the distance from the Sun at which an asteroid can retain significant amounts of ice on its surface. This is about 5AU in the current era.
You don’t want to be any further from the Sun than that.
Note that Jupiter is just about on the current snow line, so it would be too cold to live there without some sort of active heat management.
A surface which absorbs all of the sunlight hitting it, but doesn’t radiate any heat, is a physical absurdity. More realistic is to make it do both. Most realistic of all would be to have all faces of the cube do both, in which case you’ve got conditions similar to a planet.
