In this paper, we are interested in modeling the diffusion of information in a multilayer network using thermodynamic diffusion approach. State of each agent is viewed as a topic mixture represented by a distribution over multiple topics. We have observed and learned diffusion-related thermodynamical patterns in the training data set, and we have used the estimated diffusion structure to predict the future states of the agents. A priori knowledge of a fraction of the state of all agents changes the problem to be a Kalman predictor problem that refines the predicted system state using the error in estimation of the agents. A real world Twitter data set is then used to evaluate and validate our information diffusion model.