about heat

1.
Any hot body will radiate heat in form of radiation (like infra-red radiation) to the surrounding, no matter it is vaccum or not. Radiation can travel well through vaccum, just as radiation from Sun to Earth. Moreover, outer space is certainly cooler than the specific hot water.
2.
In form of radiation for the space in vaccum.
3.
Heat energy radiate from Earth to the outer space by radiation.
4.
Radiation can travel infinity in a totally vaccum, i.e. no energy lost. Lost energy only pass through matter. In fact it is possible for the space to be virtually (nearly) totally vaccum. So it is not TOTALLY vaccum, but very near to totally vaccum. As strictly totally vaccum does not make sense in the real world.
I hope this can help your understanding.

2007-11-05 10:10:00 補充：
Maybe in totally vaccum, in definition there is no mass, the entrapy define by the part E=mcΔT will be zero. But the other part of energy may still exist in that vaccum in form of radiation. Each photon exist in that particular space still carry energy.

2007-11-05 10:10:17 補充：
Moreover, totally vaccum may just only exist in definition, as there is just nearly totally vaccum. You can have nearly totally vaccum, but very hard to achieve totally vaccum.