Heat conduction is defined as the transfer of heat through matter.
This means that in space heat conduction will not work, and this comes form the fact that in space there's no matter.
Hence we have:
The procees of heat transfer by conduction would not work in space.
Claim:
Heat transfer by conduction would not work in space.
Evidence:
In the space there's no matter.
Reasoning:
Conduction needs matter to work since in space there's no matter this type of heat transfer in space.