A theoretical study of the specific heat C(T) as a function of temperature in Fibonacci magnetic superlattices is presented. We consider quasiperiodic structures composed of ferromagnetic films, each described by the Heisenberg model, with biquadratic and bilinear coupling between them. We have taken the ratios between the biquadratic and bilinear exchange terms according to experimental data recently measured for different regions of their regime. Although some previous properties of the spin wave specific heat are also reproduced here, new features appear in this case, the most important of them being an interesting broken-symmetry related to the interlayer biquadratic term.