The thermal conductivity of B-form double-stranded DNA (dsDNA) of the Drew-Dickerson sequence d(CGCGAATTCGCG) is computed using classical molecular dynamics (MD) simulations. In contrast to previous studies, which focus on a simplified 1D model or a coarse-grained model of DNA to reduce simulation times, full atomistic simulations are employed to understand the thermal conduction in B-DNA. Thermal conductivities at different temperatures from 100 to 400 K are investigated using the Einstein-Green-Kubo equilibrium and Muller-Plathe non-equilibrium formalisms. The thermal conductivity of B-DNA at room temperature is found to be 1.5 W/m.K in equilibrium and 1.225 W/m.K in the non-equilibrium approach. In addition, the denaturation regime of B-DNA is obtained from the variation of thermal conductivity with temperature. It is in agreement with previous studies using the Peyrard-Bishop-Dauxois model at a temperature of around 350 K. The quantum heat capacity (C-vq) has given additional clues regarding the Debye and denaturation temperature of 12-bp B-DNA.