Diamond growth in a hot-filament chemical vapor deposition system is investigated numerically and results are compared with experiments. The mathematical model for the description of the gas phase assumes a stagnation-point flow and the corresponding governing equations for mass, momentum, chemical species mass fractions, and energy are solved in their one-dimensional form. A detailed surface reaction mechanism for diamond growth is used which accounts for the incorporation of the CH3 radical in the diamond lattice on the reconstructed C(100) surface. This reaction scheme describes the surface-temperature dependence of the diamond growth rate correctly. In agreement with the experiment, this temperature dependence can be characterized by an apparent activation energy of about 84 kJ/mol for temperatures below 1200 K. A sensitivity analysis of the surface reaction scheme is performed to gain insight into the sources of this apparent activation energy. It is shown that a single surface reaction is responsible for the temperature dependence of the diamond growth rate.