This Thesis develops a mathematical model for predicting the thermal response in the surgical drilling of bone. The model accounts for the bone, chip and drill bit interactions by providing a detailed account of events within a cylindrical control volume enveloping the drill, the cut bone chip within the drill bit flute and the solid bone. Lumped parameter approach divides the control volume into a number of cells and cells within the sub-volumes representing the drill solid, the bone chip and the bone solid are allowed to interact. The contact mechanics of rough surfaces is used to model chip-flute and chip-bone frictional interaction. In this way not only the quantification of friction due to sliding contact of chip-flute and chip-bone rough surface contact are treated, but also the contact thermal resistances between the rubbing surfaces are included in the model. A mixed combination of constant and adaptive mesh is employed to permit the simulation of the heat transfer as the drill bit penetrates deeper into the bone during a drilling process. Using the model the effect of various parameters on the temperature rise in bone, drill and the chip are investigated. It is found that maximum temperature within the bone occurs at the location adjacent to the corner of the drill-tip and drill body. The results of the model are found to agree favorably with the experimental measurements reported in the existing literature on surgical drilling.