Marangoni convection in binary drops resting on a plate in quiescent air is studied. Water is used with low molar fractions of 2-butanol or ethanol. The droplets are homogeneously cooled from below with an initial temperature difference of 3.5 K. In the presence of air, the thermocapillary and concentration-gradients induced motions are mutually reinforcing; The latter motions last much longer than the time it takes for interfacial temperature gradients to become negligible. The Marangoni convection time increases with increasing concentration of alcohol if the volume concentration is less than 10 vol.%, levels off at higher concentrations and is higher for 2-butanol than for ethanol. The consequences for dropwise condensation in practical compact heat exchangers are investigated by measuring differences in temperature gradient histories during actual condensation processes.