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Heat loss would only be radiative, in the absence of fluid about you (air or water) there's no medium for conduction and in free fall there's no method for convection.
You also have to account for heat gain from solar radiation. Imagine the hottest day you've ever experienced. That is the heat of the sun fully attenuated by the atmosphere. In space, assuming you were in Earth orbit, you would potentially heat up faster than you'd col down, unless you were in shade.
So the answer to "how long would it take to get to 3K?" is "It depends".
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Overhead, the Albatross hangs motionless upon the air,
And deep beneath the rolling waves,
In labyrinths of Coral Caves,
The Echo of a distant time
Comes willowing across the sand;
And everthing is Green and Submarine
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