Which type of heat transfer can happen through empty space?

Answer: Heat transfer by radiation

Explanation:

There are three ways in which the thermal transfer (heat) occurs:

1. By Conduction, when the transmission is by the direct contact.

2. By Convection, heat transfer in fluids (like water or the air, for example).

3. By Radiation, by the electromagnetic waves (they can travel through any medium and in vacumm or empty space)

Since outter space is vacuum (sometimes called "empty"), energy cannot be transmitted by convection, nor conduction. It must be transmitted by electromagnetic waves that are able to travel with or without a medium.