Earlier quoted context omitted.
No, actually, a vacuum is an ideal environment for radiating heat away -- better than an atmosphere, certainly. Surfaces in lunar shadow really do drop to an extremely low temperature over a period of days.
You changed the entire context by sticking the word 'radiating' in there. Yes vacuum is fine for radiation, but radiation is much slower than physical contact with standard pressure air.
Actually, it's the other way around. Under a clear sky at the surface of the earth, radiation is much more efficient than convection and conduction to air. This is why objects at the surface readily cool below air temperature at night.
Source: http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/coobod.htm...
The linked example is a person losing heat energy under normal circumstances (23 C ambient, body temperature of 34 C). The example shows that a body loses 17 watts to perspiration, 11 watts to conduction (to the air and environment), and 133 watts to radiation.
Contrary to what many people think, a planet without an atmosphere loses heat to space very efficiently, solely by radiation -- indeed, that mechanism is more efficient in the absence of an atmosphere. But even with an atmosphere, radiation is the major heat loss mechanism, most more efficient than convection.