Recent experiments on the evaporation of sessile droplets have revealed the spontaneous formation of various patterns including the presence of hydrothermal waves. These waves had previously been observed, in the absence of evaporation, in thin liquid layers subjected to an imposed, uniform temperature gradient. This is in contrast to the evaporating droplet case wherein these gradients arise naturally due to evaporation and are spatially and temporally varying. In the present paper, we present a theory of evaporating sessile droplets deposited on a heated surface and propose a candidate mechanism for the observed pattern formation using a linear stability analysis in the quasi-steady-state approximation. A qualitative agreement with experimental trends is observed.