Dynamic effects in shallow solar stills are shown to dampen and delay the time response of state variables. The thermal inertia of these systems might reside in the glazing, in the tray materials including insulation, and even more in the brine itself. A combination of these with solar irradiance and weather conditions can conceivably enhance overall still performance, particularly if coupled with adequate operating practices. Conversely, thermal dynamic effects can combine with weather to magnify thermal losses. A numerical study, based on a lumped parameter mathematical model of the Cooper-type, reveals the expected sensitivity of productivity to the thermal capacity of the intervening elements. Sensitivity to thermal inertia results in markedly different distillate production patterns before and after noon. Variations correspond to narrow ranges of temperature differences. Weather results in variable production rates through a complex variation in temperature differences, heat transfer coefficients and initial brine depth. This paper explores the limit values these variables might attain under typical desert conditions, and the expected interaction between those variables.