Efficient thermal management of modern electronics requires the use of thin films with highly anisotropic thermal conductivity. Such films enable the effective dissipation of excess heat along one direction while simultaneously providing thermal insulation along the perpendicular direction. This study employs non-equilibrium molecular dynamics to investigate the thermal conductivity of bilayer graphene (BLG) sheets, examining both in-plane and cross-plane thermal conductivities. The in-plane thermal conductivity of 10 nm × 10 nm BLG with zigzag and armchair edges at room temperature is found to be around 204 W/m·K and 124 W/m·K, respectively. The in-plane thermal conductivity of BLG increases with sheet length. BLG with zigzag edges consistently exhibits 30–40% higher thermal conductivity than BLG with armchair edges. In addition, increasing temperature from 300 K to 600 K decreases the in-plane thermal conductivity of a 10 nm × 10 nm zigzag BLG by about 34%. Similarly, the application of a 12.5% tensile strain induces a 51% reduction in its thermal conductivity compared to the strain-free values. Armchair configurations exhibit similar responses to variations in temperature and strain, but with less sensitivity. Furthermore, the cross-plane thermal conductivity of BLG at 300 K is estimated to be 0.05 W/m·K, significantly lower than the in-plane results. The cross-plane thermal conductance of BLG decreases with increasing temperatures, specifically, at 600 K, its value is almost 16% of that observed at 300 K.