Thermal history control is performed in a thermal printer in which a single thermal print head prints sequentially on multiple color-forming layers in a single pass. Each pixel-printing interval may be divided into segments, each of which may be used to print a different color. The manner in which the input energy to be provided to each print head element is selected may be varied for each of the segments. Different energy computation functions may be used to compute the energy to be provided to the print head in each of the segments based on the predicted print head element temperature at the beginning of the segment, the color to be printed, and the energy that was supplied when printing other colors during the time period between the beginning of the segment of the current pixel-printing interval and the end of the equivalent segment of the previous pixel-printing interval.