This paper introduces simulated tempering, a Markov chain Monte Carlo (MCMC) method inspired by simulated annealing, for efficient sampling in complex statistical problems. The method involves simulating a sequence of distributions, allowing the distribution being simulated to vary randomly over time. This approach enables rapid mixing, making it suitable for problems where traditional MCMC methods would be too slow. The paper demonstrates the method's effectiveness on challenging problems, such as ancestral inference in a large genealogy involving 2024 individuals, where the goal is to compute the probability of each individual being a carrier of cystic fibrosis. The method outperforms traditional Gibbs samplers, which fail to mix in reasonable time for such problems. The paper also provides examples of simulated tempering applied to the "witch’s hat" distribution and the conditional Strauss process. The method is shown to be effective for both complex and simpler problems, addressing concerns about convergence in MCMC. The paper discusses the importance of choosing appropriate pseudo-priors and the benefits of regeneration in improving estimation accuracy. It concludes that simulated tempering offers a more efficient and reliable approach to MCMC sampling in high-dimensional problems.This paper introduces simulated tempering, a Markov chain Monte Carlo (MCMC) method inspired by simulated annealing, for efficient sampling in complex statistical problems. The method involves simulating a sequence of distributions, allowing the distribution being simulated to vary randomly over time. This approach enables rapid mixing, making it suitable for problems where traditional MCMC methods would be too slow. The paper demonstrates the method's effectiveness on challenging problems, such as ancestral inference in a large genealogy involving 2024 individuals, where the goal is to compute the probability of each individual being a carrier of cystic fibrosis. The method outperforms traditional Gibbs samplers, which fail to mix in reasonable time for such problems. The paper also provides examples of simulated tempering applied to the "witch’s hat" distribution and the conditional Strauss process. The method is shown to be effective for both complex and simpler problems, addressing concerns about convergence in MCMC. The paper discusses the importance of choosing appropriate pseudo-priors and the benefits of regeneration in improving estimation accuracy. It concludes that simulated tempering offers a more efficient and reliable approach to MCMC sampling in high-dimensional problems.