We examine the temperature evolution near horizontal drillholes designed for the disposal of spent nuclear fuel and high-level radioactive waste. In this concept, directional drilling technology is used to complete a small-diameter, vertical access hole, which at the target depth gradually turns into a horizontal section dedicated for the end-to-end disposal of nuclear waste canisters in a suitable, low-permeable formation. Decay heat emanating from the waste leads to temperature increases within the drillhole and the surrounding host rock. Predicting the thermal evolution within the engineered and natural barrier systems is important, because high temperatures may lead to thermal stresses, alter material properties, or induce driving forces that affect the migration of radionuclides along the drillhole and in the near field of the repository. We present the results of numerical design calculations that examine the spatial and temporal evolution of temperature as a function of uncertain material properties and adjustable design parameters.