Band-edge thermometry is becoming an established noncontact method for determining substrate temperature during molecular beam epitaxy. However, with this technique thin-film interference and/or absorption in the growing epilayer can cause shape distortions of the spectrum that may be interpreted erroneously as real temperature shifts of the substrate. An algorithm is presented that uses the width of the spectrum to correct for apparent temperature errors caused by interference and absorption in the epilayer. This correction procedure is tested on substrate temperature data taken during the growth of a lambda = 930 nm resonant cavity, where the apparent substrate temperature oscillates +/-5 degrees C during the growth of the mirror stacks. These oscillations are reduced to +/-3 degrees C using the correction algorithm. A recently developed model for the substrate temperature dynamics in molecular beam epitaxy shows that roughly +/-1 degrees C of the remaining +/-3 degrees C temperature oscillations are real. Band-edge thermometry is also used to control the substrate temperature to within +/-2 degrees C during the growth of near-lattice-matched InGaAs on InP, whereas the same growth under constant thermocouple temperature would result in a 50 degrees C rise in the actual substrate temperature.