We investigate to what extent the specific heat of amorphous silica can be calculated within the harmonic approximation. For this we use molecular dynamics computer simulations to calculate, for a simple silica model (the BKS potential), the velocity autocorrelation function and hence an effective density of states g(v). We find that the harmonic approximation is valid for temperatures below 300 K but starts to break down at higher temperatures. We show that, to obtain a reliable description of the low-frequency part of g(v), i.e., where the boson peak is observed, it is essential to use large systems for the simulations and small cooling rates to quench the samples. We find that the calculated specific heat is, at low temperatures (below 50 K), about a factor of 2 smaller than the experimental one. In the temperature range 200 K less than or equal to T less than or equal to T-g, where T-g = 1450 K is the glass transition temperature, we find a very good agreement between the theoretical specific heat and the experimental one.