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The model under consideration is the two-dimensional Coulomb gas of ± charged hard disks with diameter σ. For the case of pointlike charges (σ = 0), the system is stable against collapse of positive-negative pairs of charges in the range of inverse temperatures 0≤β<2, where its full exact thermodynamics was obtained recently. In the present work, we derive the leading correction to the exact thermodynamics of pointlike charges due to presence of the hard core σ which enables us to extend the treatment beyond the collapse point β = 2. Our results, which are conjectured to be exact in the low-density limit in the interval 0≤β<3, reproduce correctly the singularities of thermodynamic quantities at the collapse point and agree well with Monte-Carlo simulations. The “subtraction” mechanism within the ansatz proposed by M. E. Fisher et al. [J. Stat. Phys.79:1 (1995)], which excludes the existence of intermediate phases between the collapse point β = 2 and the Kosterlitz–Thouless transition point βKT = 4, is confirmed, however, a different analytic structure of this ansatz is suggested.