Fire dynamics in a well-confined and mechanically ventilated enclosure (a configuration of interest to the nuclear industry) strongly depends on the interaction between the fuel burning rates and the intake and exhaust volume flow rates (delivered by the fans). Several experiments show that, in the under-ventilated regime, an oscillatory behavior may be established with frequencies in the order of a few mHz. This article reports one of the first comprehensive numerical analyses performed in order to study periodic pressure and burning rate instabilities for the case of a full-scale heptane pool fire, for which experimental data has not been published yet. In the numerical analysis, carried out with the fire dynamics simulator (FDS), periodic pressure and burning rate instabilities were predicted with a frequency of approximately 10 mHz. The analysis shows evidence of the correlation between the variation of ventilation flow rates (due to pressure instabilities) and the burning rate oscillations. The latter oscillations are directly linked to oscillations in the fuel burning area attributed to the ventilation-controlled conditions.