This paper belongs to the series devoted to the calculation of particle masses in p-adic conformal field theory limit of TGD. The concept of topological condensate generalizes the concept of 3-space. Various hierarchically ordered levels of the condensate obey effective p-adic topology and fractal considerations motivate the hypothesis that physically interesting values of p correspond to primes near prime powers of two, in particular Mersenne primes. This hypothesis relates succesfully the fundamental elementary par- ticle mass scales to Planck mass scale. The fundamental description of Higgs mechanism is in terms of p-adic thermodynamics for the Virasoro generator $L^0$ (mass squared). Massivation follows from the small thermal mixing of massless ground state with Planck mass excitations. The quantization of temperature at low temperature limit gives earlier length scale hypothesis as a prediction. In this paper the general theory of Higgs mechanism is described and calculation of elementary fermion and boson masses is left to the third paper of the series.