The approach-to-equilibrium molecular dynamics (AEMD) methodology is applied in combination with first-principles molecular dynamics to investigate the thermal transfer between two silicon blocks connected by a molecular layer. Our configuration consists of alkanes molecules strongly coupled to the silicon surfaces via covalent bonds. In phase 1 of AEMD, the two Si blocks are thermalized at high and low temperatures to form the hot and cold reservoirs. During phase 2 of AEMD, a transfer between reservoirs occurs until thermal equilibrium is reached. The transfer across the interface dominates the transient over heat conduction within the reservoirs. The value of the thermal interface conductance is in agreement with the experimental data obtained for analogous bonding cases between molecules and reservoirs. The dependence on the length of the thermal interface resistance features two contributions. One is constant (the resistance at the silicon/molecule interface), while the other varies linearly with the length of the molecular chains (diffusive transport). The corresponding value of the thermal conductivity agrees well with experiments.