In this article, we develop a Triplet Markov Tree model with auxiliary random variables for an approximate inference in an intractable probabilistic model. It is based on recent advances on probabilistic modeling and varational inference with auxiliary random variables. The new Triplet Markov Tree model performs better than the classical Mean-Field variational inference and than a tree-structured variational inference. Our study provides insights and motivations for the developing workaround models involving auxiliary random variables.