Aims. We aim to measure the physical properties of the hot X-ray corona of two active galactic nuclei, NGC 4388 and NGC 2110. Methods. We analysed the hard X-ray (20–300 keV) INTEGRAL spectrum in conjunction with archival XMM–Newton and NuSTAR data. Results. The X-ray spectrum of both sources is phenomenologically well described by an absorbed cut-off power law. In agreement with previous results, we find no evidence of a Compton reflection component in these sources. We obtain a high-energy cut-off of 200₋₄₀⁺⁷⁵ keV for NGC 4388 and 320₋₆₀⁺¹⁰⁰ keV for NGC 2110. A fit with a thermal Comptonisation model yields a coronal temperature of 80₋₂₀⁺⁴⁰ keV and 75₋₁₅⁺²⁰ keV, respectively, and an optical depth of approximately two, assuming a spherical geometry. The coronal temperature and luminosity of both sources are consistent with pair production that acts as a thermostat for the thermal plasma. These results emphasise the importance of good signal-to-noise X-ray data above 100 keV to probe the high-energy emission of AGNs.