This research made a numerical analysis of the influence of the temperature on the stability of the rock slope. For this purpose, it analyzed a landslide of rock that occurred in the Rio de Janeiro, Brasil, in 2009. The studies made by Geo-Rio (Geo-Rio, 2009) after the landslide, did not find any evidence of a triggering factor, such as underground water, rainfall, overload on the top of the slope, which could be triggered the slipping; therefore was done the consideration that the triggering factor could be the fluctuation of the rock temperature. Chavez (Chavez, 2007) made an experimental study to evaluate the influence of the temperature fluctuation on the stability of the rock mass; this helped to determine the equations of the variation of the temperature, and be able to define the boundary conditions for the numerical model. The modeling was done in 3DEC software (3 Dimensional Distinct Element Code) (Itasca, 2007). The software represents the discontinuous medium such as assemblage of discrete blocks; this feature is useful because it can represent, approximately, the geometries of the slide blocks. The numerical method that 3DEC uses is the discrete element method. The analysis was done in two stages, the first stage the temperature model keeps constant, and in the second stage the temperature of the model varies with respect to time. In these two stages was also changed the angle of friction. The results indicated that when one has fluctuation of the temperature, with high frequency, and slow value of the angle friction are generated the conditions for that the slope slipping.