The quantitative approach is admirable, but Buffon's assumptions are flawed. Silicate minerals have lower heat conductivity than steels and are better insulators leading to slower cooling rates.
Second, the calculations did not incorporate the heating effects of radioactive decay.
The radiocarbon dating method is based on the fact that radiocarbon is constantly being created in the atmosphere by the interaction of cosmic rays with atmospheric nitrogen.
The resulting radiocarbon combines with atmospheric oxygen to form radioactive carbon dioxide, which is incorporated into plants by photosynthesis; animals then acquire in a sample from a dead plant or animal such as a piece of wood or a fragment of bone provides information that can be used to calculate when the animal or plant died.
Other corrections must be made to account for the proportion of throughout the biosphere (reservoir effects).