We propose a novel multi-sensor system for accurate and power-efficient dynamic car-driver hand-gesture recognition, using a short-range radar, a color camera, and a depth camera, which together make the system robust against variable lighting conditions. We present a procedure to jointly calibrate the radar and depth sensors. We employ convolutional deep neural networks to fuse data from multiple sensors and to classify the gestures. Our algorithm accurately recognizes 10 different gestures acquired indoors and outdoors in a car during the day and at night. It consumes significantly less power than purely vision-based systems.