An electronic device may be provided with proximity sensor capabilities for monitoring for the presence of nearby external objects. The electronic device may make temperature measurements such as measurements involving the monitoring of nearby objects for emitted blackbody light indicative of whether or not the external object is a heat-emitting object such as a human body part. The same sensor that is used in gathering temperature readings may be used in gathering proximity sensor data or separate temperature sensor and proximity sensor detector structures may be used. Motion sensor capabilities may be provided using sensor structures having an array of heat sensing elements. Signals from the array of heat sensing elements may be used in making temperature measurements and in gathering proximity sensor readings. Sensor structures may operate at wavelengths longer than 3 microns such as wavelengths from 3-5 microns or 10-15 microns.