We propose the strategic scheduling problem of an energy utility that administers a large residential population and may ask individual consumers to curtail part of their HVAC usage profile up to a certain effort budget, in such a way that the aggregate reductions follow a desired day-ahead goal profile. Each consumer is described by a forecast of their thermal response profile computed using a statistical model that decomposes smart meter data into a thermally-sensitive component and an intentional usage component. We propose an algorithm for computing individually-tailored optimal action schedules (e.g., automated Demand-Response control or marketing calls) for thermal energy consumption for a large sample of consumers that is based on solving a convex program. Then, we describe an approximate version of the original scheduling problem that is both interpretable and faster to compute. For this, we recast strategic scheduling as a discrete, set selection problem in which the operator is constrained by what effort structures it can request from the consumers. We propose an efficient algorithm for selecting optimal sets of consumers based on optimizing non-monotone submodular functions.