What type of heat does not require matter?

It would be Thermal Radiation

Radiation is the only method of heat transfer that does not require matter.

Facts about Radiation :

The energy from the sun is received in the form of radiation. It travels in the form of waves. It can be absorbed by substances in its path.Heat Radiation travels through air. Black surfaces are the emitters of heat radiation.Shiny surfaces are the reflectors of heat radiation.Heat transfer by Radiation doesn't require any medium.