Earth gets its warmth from the sun and its cold from space. Both are important.
Energy flow outwards equals energy flow in, and this ensures that the planet's
temperature stays constant. But the outflowing energy carries more entropy with
it than the incoming energy did. It's this entropy difference that all life on
Earth relies on to survive. We couldn't live without the cold night sky, just
like we couldn't live without the sun.

Could we run a heat engine off the difference between the temperature of space 
the local ambient temperature here on Earth? In theory, yes. In practice, the
atmosphere gets in the way, preventing us from building radiators that directly
emit into space. Let's say we build a radiator pointed up at the sky. The
atmosphere is going to absorb some of the photons that it emits, and is going
to emit some photons of its own, heading back downards into the radiator. This
prevents the radiator from getting properly cool, though some amount of cooling
is going to happen. If you set up some filters and are careful about which
frequencies you bounce off and which you let through, you might be able to get
it even colder. Still nowhere close to the actual temperature of space, though.
If only there were some way to bypass the atmosphere entirely...

Gravitational waves go straight through most things. What if we could build a
radiator that emitted gravitons rather than photons? That would certainly solve
the problem of bypassing the atmosphere. But it would be impossible to build
such a radiator. The whole reason that gravitons make for a good way of getting
past the atmosphere is that they aren't going to be emitted and absorbed by the
atmosphere. Gravitational waves tend to be made by things like black holes and
neutron stars colliding with each other. I.e. they require large amounts of
energy moving around at high speeds. We aren't going to be able to build that.
And to make a proper radiator, entropy in the radiator has to somehow end up in
the gravitational waves heading out of the device. It can't just make the waves,
those waves have to be thermal noise. So it seems like we're stuck with electro-
magnetic radiation as our cooling method for the forseeable future.