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The double phase transition of hadronic matter, $H$, first, to the gas ofdeconfined constituent quarks (for brevity called {\it valons}), $Q$, and then,secondly, the phase transition from $Q$ to quark-gluon plasma, $QGP$, isconsidered within bag model ideology. In distinction from previous double phasetransition investigations, it is not supposed that at zero chemical potential(~$\mu=0$~) transition temperatures $T_d$ (for $H~\leftrightarrow~Q$) and$T_{ch}$ (for $Q~\leftrightarrow~ QGP$, chiral restoration) coincide. Then forplausible range of chosen bag constants, $B_Q$ for $Q$ and $B_q$ for $QGP$ thephase transition $H~ \leftrightarrow~ QGP$ can proceed {\it only via the $Q$phase} (at least at not too much $\mu$). For small $\mu$ the gap,$T_{ch}~-~T_d$, is quite essential, up to $\approx~50$ MeV. The physicalmeaning of the $H~ \leftrightarrow~ Q$ transition temperature, $T_d$, coincidewith that of the Hagedorn temperature, $T_H$.

Deconfinement of Constituent Quarks and the Hagedorn Temperature