Midlatitude cyclones with characteristics similar to tropical cyclones (also known as Tropical‐Like Cyclones, TLCs, or medicanes) are sometimes observed in the Mediterranean region. The Wind Induced Surface Heat Exchange (WISHE) mechanism has been considered responsible for their development, in analogy with tropical‐cyclone theory. However, some recent papers have proposed a different explanation, suggesting that the deep warm core in the TLC is mainly an effect of the seclusion of warm air in the cyclone core. To investigate the latter hypothesis, two case‐studies of Mediterranean TLCs are analysed here by means of high‐resolution numerical experiments. The evolution of the near‐surface equivalent potential temperature is followed along back‐trajectories around the cyclone centre, showing for both cases a strong heating when the parcel moves from the outer part of the cyclone to its inner, warmer core. Sensitivity experiments clarify the mechanism of cyclone intensification and the way the warm‐core structure is generated, showing that sea‐surface fluxes and/or condensation latent heating are fundamental to explain the intensification of the cyclones. However, the importance of air–sea interaction processes is case dependent. For the first cyclone, the intense sea‐surface fluxes, associated with tramontane and cierzo winds over the western Mediterranean Sea, transfer a large amount of energy from the ocean to the atmosphere in the area where the cyclone developed, so that the vortex is able to sustain itself in a barotropic environment and reach a tropical‐like structure at a later stage in its lifetime. For the second cyclone, the cyclone never develops a fully tropical‐like structure, evolving in the baroclinic environment associated with the potential vorticity streamer in which the cyclone formed. Based on the distinction emerging in this and other articles, a classification of medicanes in three different categories is proposed.