The temperature field inside an evaporating two-dimensional droplet resting on curved or flat isothermal substrates is studied under various evaporation conditions. An analytical solution for the temperature is derived, which can be directly used in the cases of pinned and depinned contact lines as well as in stick-slip evaporation modes. It is found that the temperature drop at the free surface of a droplet on a convex, hydrophobic substrate is far greater than that for flat or concave substrates of the same hydrophobicity. The analytical solution for the temperature field allows the direct estimate of the local temperature gradient and, hence, of the local surface tension gradient that gives rise to Marangoni flow directed from the contact lines to the top of the droplet.