In the process of drying, thin volatile liquid films often undergo a long-wavelength instability leading to nonuniformities or formation of dry spots, with the strength of the instability increasing with the volatility and temperature of the liquid. Perhaps counterintuitively, this evaporative instability can be actively suppressed by an appropriate heating procedure. We use linear stability analysis of the lubrication approximation to show that spatially nonuniform time-dependent radiative heating can indeed have a stabilizing effect. Evaporation is shown to introduce several fundamentally new aspects into the control problem for heated liquid films, compared to the relatively well-studied case of thermal convection. The control problem becomes especially interesting and nontrivial for mixtures and solutions with negative Marangoni numbers due to a peculiar cancellation effect rendering the system insensitive to temperature control at a certain wavelength. It is shown that taking the time dependence of the mean thickness of the film into account is necessary to circumvent this insensitivity.