A steady Rankine-like vortex model of a dust devil is reported, which takes into account the sunlight absorption by airborne dust particles and the diabatic heating of a rotating dust column. For the maximum swirl velocity being a few times larger than the mean updraft velocity, the model admits significant simplifications allowing for its complete analytical treatment. The competitive effects of (i) the surface heat fluxes and (ii) the suspended-dust-caused diabatic heating on the vortex constitution (strength, height and shape) are examined. The second factor is found to be more influential for the strongest vortices. A reference exponential distribution of dust devils over their radius (visible diameter), which was introduced based on general arguments of mathematical information theory, is shown to fit satisfactory well the observational data on dust devils in Arizona and southern California and, in a preliminary way, on Mars.