Seems the answer is that you don't need matter for heat radiation.
Space is cold, but it doesn't feel cold.
Fans/blowers can drive covection artificially, though.
Convection (natural or artificial) doesn't work in the absence of a convecting fluid, even when not in free-fall.
Definitely not space: https://www.youtube.com/watch?v=xdJwG_9kF8s from about the 3 min 40 second mark.
(FWIW, the slinky stuff is also really cool; weight -- in the contact[1] sense but not in the mg sense -- is dissipational, and it's nice to see that demonstrated, so I'm glad your comment caught my attention.)
> space does not feel cold
If any part of you which you expose to space (if it's shielded from solar heating, etc.) is moist -- your skin, your eyes, your tongue, the insides of your nose -- you will feel that part getting cold very quickly thanks to evaporative cooling, which works very well in free-fall and in the absence of a convecting fluid.
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[1] http://math.ucr.edu/home/baez/physics/General/Weight/whatIsW...
Normal convective cooling (think your computers CPU or your phone's backside) or evaporative cooling (sweat on your skin, discardable heatsinks) work by transferring heat to some medium. In case of CPUs you do it twice, once from CPU to metal and then from metal to Air to get a larger cooling surface.
In space you don't get that, or atleast not without having it be expensive af. The only way to loose heat energy is by radiating it away naturally (infrared light that our bodies like to emit carries heat away from our body).
This is very slow and requires a very different cooler design and some design metrics overall (if your CPU points it's heat surface at some other components of the craft, that component might overheat due to that).