An important unanswered question in planetary science is how planetesimals, the ~1–100 km solid precursors to asteroids and planets, were heated in the early Solar System. This thesis quantifies one possible heat source: planetesimal collisions. Recent work has predicted that collision velocities and planetesimal porosities were likely to have been higher than previously thought; this is likely to have significant implications on collision heating. The approach adopted in this research was to numerically model shock heating during planetesimal collisions. Simulations showed that an increase in porosity can significantly increase heating: in a 5 km s-1 collision between equal sized, non-porous planetesimals, no material was heated to the solidus, compared to two thirds of the mass of 50% porous planetesimals. Velocity also strongly influences heating: at 4 km s-1, an eighth of the mass of 50% porous planetesimals was heated to the solidus, compared to the entire mass at 6 km s-1. Further simulations quantified the influence on heating of the impactor-to-target mass ratio, the initial planetesimal temperature and the impact angle. A Monte Carlo model was developed to examine the cumulative heating caused by a population of impactors striking a parent body. In the majority of collisions the impactor was much smaller than the parent body, and only minor heating was possible. However, some larger or faster impactors were capable of causing significant heating without disrupting the parent body; these collisions could have heated up to 10% of the parent body to the solidus. To cause global heating, the collision must have catastrophically disrupted the parent body. The increase in specific internal energy from collisions was compared with the decay of short-lived radionuclides. In the first ~6 Ma, radioactive decay was the most important heat source. After ~10 Ma, the energy caused by collisions was likely to have overtaken radioactive decay as the dominant source.