We present a detailed study of the temperature evolution of the crystal structure, specific heat, magnetic susceptibility and resistivity of single crystals of the paradigmatic valence-fluctuating compound EuIr$_2$Si$_2$. A comparison to stable-valent isostructural compounds EuCo$_2$Si$_2$ (with Eu$^{3+}$), and EuRh$_2$Si$_2$, (with Eu$^{2+}$) reveals an anomalously large thermal expansion indicative of the lattice softening associated to valence fluctuations. A marked broad peak at temperatures around 65-75 K is observed in specific heat, susceptibility and the derivative of resistivity, as thermal energy becomes large enough to excite Eu into a divalent state, which localizes one f electron and increases scattering of conduction electrons. In addition, the intermediate valence at low temperatures manifests in a moderately renormalized electron mass, with enhanced values of the Sommerfeld coefficient in the specific heat and a Fermi-liquid-like dependence of resistivity at low temperatures. The high residual magnetic susceptibility is mainly ascribed to a Van Vleck contribution. Although the intermediate/fluctuating valence duality is to some extent represented in the interconfiguration fluctuation model commonly used to analyze data on valence-fluctuating systems, we show that this model cannot describe the different physical properties of EuIr$_2$Si$_2$ with a single set of parameters.
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