We present semipermeable, hollow capsules (colloidosomes) that expand and contract upon heating and cooling. The capsules are composed of micrometer-sized poly(N-isopropylacrylamide)-co-acrylic acid microgel particles, which exhibit a reversible size transition near 34 degrees C. The microgel particles assemble on the surfaces of water droplets in oil. Addition of the diblock copolymer poly(butadiene-b-N-methyl 4-vinyl pyridinium iodide) to the oil results in soft, elastic membranes of microgel particles that remain intact after the droplet interfaces are dissolved. Under heating, the capsules contract reversibly by 13% or irreversibly by 40% in radius. These stimulus-responsive colloidosomes might be useful for controlled release or as microscopic actuators.