Heat can still leave parts in space by radiating the heat away. We don't usually think about it because it's generally much slower than convective cooling here on Earth but it does happen and doesn't require a medium to cool. It's the method the ISS uses to cool its interior for example. [1]
Unfortunately it's too slow. I work with electron beam welders so this is an everyday problem as it takes place in a high vacuum (1e-3 Torr or lower). Though for welding it usually isn't a big issue as most parts are large enough to sink their own heat. For deep high power welds in material which can't sink the heat we attach copper heat sink blocks to soak up heat like a sponge or for extreme cases, circulated oil cooled heat sinks.
In space you can't vent to atmosphere or run the oil through a fan/water cooled radiator. So I'm thinking you'd have to build a heat reclaimer or high surface area radiator which uses an active cooling system like thermal pipes or circulated fluids like oil. But how does this adapt to different parts with odd shapes? Perhaps the printing would have to take place in a pressurized environment to facilitate cooling using gas and then figure out how to get rid of or recycle the waste heat.
Depending on the conductivity of the material being used could you not have it sink it's own heat through conduction into a pad connected to a beefier version of the ISS ammonia to radiator cycle or combine it with a phase change cooler that melts wax into liquid then slowly radiates that heat away? Even in an atmosphere you have to deal with all that heat eventually.
Truthfully I don't think the best way would even be to try to 3D print the whole structure though just generic pieces that are then assembled into larger assemblies. Just being able to mass manufacture extruded profiles and sheet metal would allow you to do a lot in space that would be hard to launch piecemeal from the ground. Then smaller specialized pieces to join them together in the specific way required for the current vehicle being built could be printed and assembled.
There's a lot of neat research going on in assembling structures like that atm.
well, it depends on the target temperature you want to maintain. Radiative power grows with the forth power of temperature (https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law). So that red glow of Merlin engines mentioned by the other comenter radiates so intensively that any other method of heat transfer can hardly come close. Another example - just 5700K of the Sun surface is enough to radiate away all the power the Sun's body generates.
The upper stage variant of the Merlin engine used on Falcon 9 uses radiative cooling as well - that's why it's nozzle extension glows red hot - it cools itself that way! :-)
right, but the rate of dissipation would be a huge problem for the additive technique described in this article. Plus the lack of gravity means that the molten metal would adhere to the existing component very very differently. Essentially it would mean designing the process from scratch - with almost no ability to test on earth during the design process. Not sure how effective computer modelling is for that type of thing :)
You can do small scale tests of each bit though: testing the sintered powder jet on a parabolic flight, test the heat dissipation in a vacuum chamber, etc. It wouldn't be easy but it's far from impossible.
[0] https://en.wikipedia.org/wiki/Radiative_cooling
[1] https://science.nasa.gov/science-news/science-at-nasa/2001/a...