Embedded AI is moving from perception to prediction. Robots now use world models$\unicode{x2014}$learned simulators that predict the outcome of candidate actions in a compressed latent space before any is executed. Every predicted step must be computed on board within a tight power and thermal budget, yet the energy these steps fundamentally require, and how far real hardware sits from it, have not been characterized. We derive lower bounds on the arithmetic operations and the CMOS dynamic energy of a latent state transition from information theory and Boolean circuit complexity. Profiling a DreamerV3-style Recurrent State Space Model (RSSM) shows that every rollout operation is memory-bandwidth bound and that a GPU consumes at least $5.9\times10^{10}$ times the CMOS energy floor. Transient 3D thermal simulations show that this inefficiency is also a thermal one, since sustained back-to-back planning heats a millimeter-scale silicon tile to 556 K even behind an ideal copper heat spreader. Guided by this chain from bound to bottleneck, we propose the World Model Planning Accelerator (WMPA), a chip architecture for embedded world model planning that combines near-memory computation, real-time entropy estimation, variable-precision rollout units, and copy-on-write latent scratchpads. With a design target of 40x lower power, the same tile stays near ambient at 306 K in simulation, pointing toward practical planning on thermally constrained robots.

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