How is heat transferred through empty space?
I would say through Radiation.
Heat is basically Energy in motion.
Energy can "move" in various ways:
Radiation relies on propagation of Electromagnetic Radiation; basically waves, such as light, x-rays, u-v or infrared, are electromagnetic waves that transport energy.
These waves can travel through vacuum because they do not need a material medium (as in sound waves) to propagate but are a perturbation of the electromagnetic field.
Each wave will carry energy in the form of...packets called Photons (kind of a rain of "droplets" of light!!!).
Each photon carries an energy:
So you see that the higher the frequency the higher is the energy.