Cooling via radiation is relatively slow compared to convection, but remember, your background is essentially -270 degrees. Radiative cooling scales with the temperature difference to the fourth, so it’s not as weak as you may think.
When cooling *does* become an issue, large black radiator panels are an option. These radiate heat away quickly, so if heat can be transported to these panels it radiates away much quicker than it would from the craft body.
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