A molecular dynamics simulation was performed to study the effect of an applied force on heat transfer at the interface of model diamond {111} nanosurfaces. The force was applied to a small, hot nanosurface at 800, 1000, or 1200 K brought into contact with a larger, colder nanosurface at 300 K. The relaxation of the initial nonequilibrium interfacial force occurs on a subpicosecond time scale, much shorter than that required for heat transfer. Heat transfer occurs with exponential kinetics and a rate constant that increases linearly with the interfacial force according to 7 x 10(-4) ps(-1)/nN. This rate constant only increases by at most 10% as the temperature of the hot surface is increased from 800 to 1200 K. Replacing the interfacial H-atoms on both surfaces by D atoms also has a very small effect on the heat transfer. However, if one nanosurface has H atoms on its interface and the other nanosurface's interface has D atoms, then there is a marked 25% decrease in the rate constant for heat transfer. Increasing, the size of the hot surface, and, thus, the interfacial contact area, increases the rate of heat transfer but not the rate constant. For the same interfacial force, different anharmonic models for the nanosurfaces' potential energy function give the same heat transfer rate constant. The possibility of quantum effects for heat transfer across the diamond interface is considered.