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The cosmonauts from Soyuz T-13 mission "wore winter garb, including fur-lined hats, as they entered the station." "Frost covered the walls and apparatus. "

Essentially, the heat balance of Salyut 7 was definitely negative, requiring active heating.

Meanwhile, ISS requires active cooling, and a lot of it, suffering from surplus heat, the radiators and cooling systems being absolutely vital to the station's existence.

Would ISS freeze over as well, without power? Or do the two designs differ in some significant way that changes their "ambient" temperature?

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Salyut 7 had a active cooling system as well. The heat exchangers are the large white panels, perpendicular to the solar panels, to be seen in photographs of the station. This is necessary on all space stations in active mode as the energy produced by solar panels (apparently 4.5 kW in case of Salyut 7, an order of magnitude more in case of the ISS) needs to be dissipated in some way. The only natural way of cooling a station is by radiation - and this is not a lot: An ideal radiator can emit about 400 W/m² at room temperature while sun delivers almost 1400 W to the same surface.

The reason for the station to be freezing cold when Soyuz T-13 arrived is that at this point the station was completely without power for almost four months. The only energy heating up the station was sun light. During night, the station lost heat by radiation. The exact equilibrium temperature can not be easily calculated and depends a lot on surface area, volume, attitude and shielding of the station. It also depends on the exact design of the cooling system - if parts of it work without electricity (e.g. by heat conductivity, not requiring pumps for a cooling liquid) it will continue to cool down the station.

It is very likely that the same freezing temperatures would be found on ISS given it was shut down completely for a longer term.

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    $\begingroup$ A further confirmation of your explanation: Apollo 13 got really cold when they did a drastic power-down. $\endgroup$ – Organic Marble Jul 23 '16 at 23:49
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A space station must expel the heat from its electronics. This heat can be considerable, which usually requires large radiators. If the station is dead, then the heat is expelled, without having the heat from the electronics to power it.

Also, Salyut 7 was designed to have constant hot water available for the astronauts. The heat from this needed to be removed, and would have been accounted for in the design.

Keep in mind the ISS requires 75-90 kW of power to function. This power will almost entirely end up as heat in the station. The ISS insulation is somewhat better than earlier stations as well, which leads to more trapped heat.

Just to give you an idea, the ISS has partially lost power for an entire day; in fact, several times. During those times, some of the internal heaters are shut off. The environment is extremely complex; without proper thermal management there would be a huge temperature swing!

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  • $\begingroup$ "Also, Salyut 7 was designed to have constant hot water available for the astronauts" why? Seems a weird requirment for a space station... $\endgroup$ – Caridorc Jul 23 '16 at 15:12
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    $\begingroup$ @Caridorc: Not for Russians ;-) $\endgroup$ – SF. Jul 23 '16 at 19:20
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    $\begingroup$ @Caridorc Probably for the баня. $\endgroup$ – Michael Hampton Jul 24 '16 at 5:19
  • $\begingroup$ "Seems a weird requirment for a space station" - Does it mean that other space stations of its time (Skylab?) did not have hot water supply, i. e. cosmonauts/astronauts were required to wash themselves with cold water? $\endgroup$ – DP_ Jul 24 '16 at 8:19

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