Organic phase change materials are usually insulating in nature, and they are unlikely to directly trigger latent heat storage through an electrical way. Here we report a multifunctional phase change composite in which the energy storage can be driven by small voltages (e.g., 1.5 V) or light illumination with high electro-to-heat or photo-to-thermal storage efficiencies (40% to 60%). The composite is composed of paraffin wax infiltrated into a porous, deformable carbon nanotube sponge; the latter not only acts as a flexible encapsulation scaffold for wax but also maintains a highly conductive network during the phase change process (for both solid and liquid states). Uniform interpenetration between the nanotube network and paraffin wax with high affinity results in enhanced phase change enthalpy and thermal conductivity compared to pure paraffin wax. Our phase change composite can store energy in practical ways such as by sunlight absorption or under voltages applied by conventional lithium-ion batteries.