Context. Warm coronas offer a plausible explanation behind the soft X-ray excess in active galactic nuclei (AGNs). This paper presents the self-consistent modeling of an accretion disk with an optically thick corona, where the gas is heated by magneto-rotational instability dynamo (MRI) and is simultaneously cooled by radiation which undergoes free-free absorption and Compton scattering. Aims. We determined the parameters of a warm corona in an AGN using disk-corona structure model that takes into account magnetic and radiation pressure. We aim to show the role of thermal instability (TI) as a constraint for warm, optically thick X-ray coronas in AGNs. Methods. With the use of relaxation code, we calculated the vertical solution of the disk driven by MRI, together with radiative transfer in hydrostatic and radiative equilibrium. This has allowed us to point out how TI affects the corona for a wide range of global parameters. Results. We show that magnetic heating is strong enough to heat the upper layers of the accretion disk atmosphere, which form the warm corona covering the disk. Magnetic pressure does not remove TI caused by radiative processes operating in X-ray emitting plasma. TI disappears only in case of accretion rates higher than 0.2 of Eddington, and high magnetic field parameter α_B > 0.1. Conclusions. TI plays the major role in the formation of the warm corona above magnetically driven accretion disk in an AGN. The warm, Compton cooled corona, responsible for soft X-ray excess, resulting from our model typically exhibits temperatures in the range of 0.01–2 keV and optical depths of even up to 50, in agreement with recent observations.