Diamond is hard and graphite is soft. Graphite is a good conductor of electricity as it has one free electron which is responsible for the conduction.
Diamond has higher thermal conductivity than graphite because the structure of diamond is precise and thus the transfer of heat is faster in it. In case of graphite, the $C - C$ bond has a double bond character so its bond order becomes higher than that of diamond which has only single $C-C$ bonds.