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We have shown in detail that the low-temperature expansion for thenon-perturbative gluon pressure has the Hagedorn-type structure. Itsexponential spectrum of all the effective gluonic excitations are expressed interms of the mass gap. It is this which is responsible for the large-scaledynamical structure of the QCD ground state. The non-perturbative gluonpressure properly scaled has a maximum at some characteristic temperature$T=T_c = 266.5 \ \MeV$, separating the low- and high temperature regions. It isexponentially suppressed in the $T \rightarrow 0$ limit. In the $T \rightarrowT_c$ limit it demonstrates an exponential rise in the number of dynamicaldegrees of freedom. Its exponential increase behavior with temperature is validonly up to $T_c$. This makes it possible to identify $T_c$ with theHagedorn-type transition temperature $T_h$, i.e., to put $T_h=T_c$ within themass gap approach to QCD at finite temperature. The non-perturbative gluonpressure has a complicated dependence on the mass gap and temperature near$T_c$ and up to approximately $(4-5)T_c$. In the limit of very hightemperatures $T \rightarrow \infty$ its polynomial character is confirmed,containing the terms proportional to $T^2$ and $T$, multiplied by thecorresponding powers of the mass gap. \end{abstract}

The Hagedorn-type structure of the non-perturbative gluon pressure within the mass gap approach to QCD