Diamond is not a good conductor of heat and electricity. Since carrier of electricity is free electron and in diamond, all the four valence electrons of carbon are involved in carbon- carbon bonding so there is no free electron for conduction.
Diamond is made up of carbon atoms bind together by strong covalent bond in tetrahedral arrangement. Due to this strong covalent bond electrons are localised (free electrons are not there), and thus diamond is bad conductor of electricity.
But diamond is good conductor of electricity by molecular vibration. This property is used in jewellery shop to distinguish between diamond and its imitators.