Question

Radiation transfers energy by waves. These waves transfer energy from a warmer object to a cooler object, with or without .

Answer 1

Radiation transfers  thermal  energy by electromagnetic  waves. These waves transfer energy from a warmer object to a cooler object, with or without  matter .

Answer 2

Hello there,

They transfer the energy with or without medium (MATTER)

Since radiation is transferred through wave, it does not need any form of objects to pass through.
For example, the heat that radiation through the sun could be felt without any objects that connect us from The sun itself.