Empty space itself cannot have a temperature, unless you mean some
abstruse question about quantum vacuums.

However, if you put a physical object into space, it will reach a
temperature that depends on how efficiently it absorbs and emits
radiation and on what heating sources are nearby.  For example, an
object that both absorbs and emits perfectly, put at the Earth's
distance from the Sun, will reach a temperature of about 280 K or 7 C.
If it is shielded from the Sun but exposed to interplanetary and
interstellar radiation, it reaches about 5 K.  If it were far from all
stars and galaxies, it would come into equilibrium with the microwave
background at about 2.7 K.

Spacecraft (and spacewalking astronauts) often run a bit hotter than
280 K because they generate internal energy.  Arranging for them to
run at the desired temperature is an important aspect of design.

Some people also consider the "temperature" of high energy particles
like the solar wind or cosmic rays or the outer parts of the Earth's
atmosphere.  These particles are not in thermal equilibrium, so it's
not correct to speak of a single temperature for them, but their
energies correspond to temperatures of thousands of kelvins or higher.
Generally speaking, these particles are too tenuous to affect the
temperature of macroscopic objects.  There simply aren't enough
particles around to transfer much energy.  (It's the same on the
ground.  There are cosmic rays going through your body all the time,
but there aren't enough to keep you warm if the air is cold.  The air
at the Earth's surface is dense enough to transfer plenty of heat to
or from your body.)