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This is the last in a series of papers on the topological susceptibility inthe interacting instanton liquid model (IILM). We will derive improved finitetemperature interactions to study the thermodynamic limit of grand canonicalMonte Carlo simulations in the quenched and unquenched case with light,physical quark masses. In particular, we will be interested in chiral symmetrybreaking. The paper culminates by giving, for the first time, a well-motivatedtemperature-dependent axion mass. Especially, this work finally provides acomputation of the axion mass in the low temperature regime, $m^2_a f^2_a =1.46 10^{-3}\Lambda^4 \frac{1+0.50 T/\Lambda}{1+(3.53 T/\Lambda)^{7.48}}$. Itconnects smoothly to the high temperature dilute gas approximation; the latteris improved by including quark threshold effects. To compare with earlierstudies, we also provide the usual power-law $m^2_a = \frac{\alpha_a\Lambda^4}{f_a^2 (T/\Lambda)^n}$, where $\Lambda=400\units{MeV}$, $n=6.68$ and$\alpha=1.68 10^{-7}$.

The topological susceptibility from grand canonical simulations in the interacting instanton liquid model: chiral phase transition and axion mass