This paper describes a new hierarchical temporal Bayesian model and a Markov chain Monte Carlo (MCMC) algorithm for gene factor analysis. Each data sample is decomposed as a linear combination of characteristic gene signatures (also called factors) with appropriate proportions, or factor scores, following a linear mixing model (LMM). The particularity of the proposed algorithm is that the LMM model is combined with a hidden Markov model (HMM) to take into account temporal dependencies between the samples. The proposed HMM structure is motivated by the behavior of host molecular response following exposure to an infectious agent. The complexity of the posterior distribution resulting from the proposed HMM is alleviated by using a hybrid Gibbs sampler that generates samples distributed according to this distribution. These samples are then used to approximate the standard Bayesian estimators of the unknown parameters. The performance of the proposed method is illustrated by simulations conducted on synthetic data and on a real public dataset.