Autoregressive language models are next-token predictors and have been criticized for only optimizing surface plausibility (i.e., local coherence) rather than maintaining correct latent-state representations (i.e., global coherence). Because Theory of Mind (ToM) tasks crucially depend on reasoning about latent mental states of oneself and others, such models are therefore often thought to fail at ToM. While post-training methods can improve ToM performance, we show that strong ToM capability can be recovered directly from the base model without any additional weight updates or verifications. Our approach builds on recent power-sampling methods (Karan & Du, 2025) that use Markov chain Monte Carlo (MCMC) to sample from sharpened sequence-level (rather than token-level) probability distributions of autoregressive language models. We further find that incorporating annealing, where the tempered distribution is gradually shifted from high to low temperature, substantially improves ToM performance over fixed-temperature power sampling. Together, these results suggest that sampling-based optimization provides a powerful way to extract latent capabilities from language models without retraining.