Effusion cells are commonly used in solid-source molecular beam epitaxy for evaporation of the source materials. A prominent inaccuracy during effusion cell operation is strong flux transients after shutter opening. We have studied the temperature and time dependent beam fluxes of effusion cells filled with the group III elements indium, aluminum, and gallium. A flux reduction due to the shutter transient up to 33% with time constants ranging from 25 to 100s is observed. A simple model of the shutter-transient behavior is proposed that well reproduces major features of the experiments. As a key point, we do not model the effusion cell simply as a Knudsen cell, but assume instead more realistic Langmuir evaporation. Our calculation results establish that heat loss due to thermal radiation from the source material surface is responsible for the shutter transient. Two applications are presented. First the calibration of beam fluxes under consideration of the shutter transient and second a technique for the compensation of the shutter transient by an optimized temperature control.