A display may receive image data to be displayed for a user of an electronic device. Display driver circuitry in the display may analyze the data to detect static data. The image data may contain static frames of data or static portions of a frame of data. In response to detection of static data, the display driver circuitry can take actions to avoid display damage due to burn-in effects. The display driver circuitry may reduce a peak luminance value associated with a peak luminance control algorithm, may reduce display brightness, may map image data to reduced brightness levels, or may take other actions to ensure that display pixels in the display are not damaged. Temperature information may be used in determining how to classify information as static data and in determining how significantly to reduce display pixel drive currents in response to the detection of static image data.