In a previous work, I discussed the effect of the primordial black holes (PBH's) quantum evaporation on the reionization of the Universe at small redshifts (z ≤ 60): in principle, the photons emitted during the evaporation of such objects could drive a new ionization for the Universe after the recombination epoch; this reionization process should happen during the last stages of the PBH's life, when they totally evaporate and emit a lot of massive and massless particles. The critical mass of a black hole whose lifetime is equal to the present age of the Universe is ~ 4.4 × 1014 h-0.3 g: thus, PBH's having a mass M ~ 1014 g are the ideal candidates to induce a reionization at small redshifts. While in my previous study, I considered an exact blackbody photon emission spectrum, here I will adopt a more realistic one, taking into account the quarks and gluons jets emission through the contribution of a known fragmentation function. When the BH temperature rises above the QCD confinement scale, ΛQCD, one should expect an important contribution from quarks and gluons emission in the form of jets. In this paper I also improved my analysis by considering without any approximation the cooling effects in the plasma temperature evolution; as a result, I obtained a satisfactory "late and sudden" reionization process, characterized by a very well controlled rise of the plasma temperature: the plasma heating is not so high to induce a strong distortion of the CBR spectrum, in agreement with the recent FIRAS upper limit on the comptonization parameter, yc < 2.5 × 10-5.