Fast optical self-focusing has been observed in a homeotropic nematic liquid crystal cell. This nonlinearity is induced by an intensity modulated infrared laser having a peak power of 160mW, a pulse repetition rate of 150Hz, and a duty cycle of 0.05 and launched with extraordinary polarization. During these experiments the illumination time is kept at 0.3msec and the ambient temperature is controlled. We have observed that self-focusing propagation depends on ambient temperature, laser power and duty cycle. Notably, when illuminating with a continuous beam having the same corresponding average power, only diffraction can be observed. These results suggest that the nonlinearity is produced by a combination of thermal effects and molecular reorientation that leads to changes in the order parameter. Further optical experiments and thermal calculations have been conducted to identify the responsible mechanism for the self-focusing of the laser beam. It has been found that soliton formation can be achieved if the parameters as ambient temperature, pulse repetition rate and duty cycle of the laser are set to optimal conditions. Although, this nonlinearity in a liquid crystal cell has been already demonstrated for transverse illumination, the presence of beam propagation with self-focusing has not been reported yet. The fast nonlinearity reported in this work has the potential to generate a number of new applications of liquid crystals.