High performance active materials are of rapidly growing interest for applications including soft robotics, microfluidic systems, and morphing composites. In particular, paraffin wax has been used to actuate miniature pumps, solenoid valves, and composite fibers, yet its deployment is typically limited by the need for external volume constraint. We demonstrate that compact, high-performance paraffin actuators can be made by confining paraffin within vertically aligned carbon nanotube (CNT) films. This large-stroke vertical actuation is enabled by strong capillary interaction between paraffin and CNTs and by engineering the CNT morphology by mechanical compression before capillary-driven infiltration of the molten paraffin. The maximum actuation strain of the corrugated CNT-paraffin films (∼0.02-0.2) is comparable to natural muscle, yet the maximum stress is limited to ∼10 kPa by collapse of the CNT network. We also show how a CNT-paraffin film can serve as a self-activating thermal interface that closes a gap when it is heated. These new CNT-paraffin film actuators could be produced by large-area CNT growth, infiltration, and lamination methods, and are attractive for use in miniature systems due to their self-contained design.