Periodically modulated time-varying media can enable a wide range of functionalities such as frequency translation and nonreciprocal scattering by allowing energy to be injected into the light field through an external modulation. However, demonstrations of such energy transfer have so far relied almost exclusively on fast periodic modulations, which are experimentally demanding. In this work, we show adiabatically slow two-parameter modulation can also perform net work on light. We use a scattering-matrix-based theory to identify the geometric origin of this adiabatic energy transfer, predict optimal wavefronts and temporal modulations that maximize this energy transfer, and validate numerically with examples in opto-mechanics and time-varying photonic media.