In this talk we study small time asymptotic of the heat content for a smoothly bounded domain with non-characteristic boundary in the Heisenberg group, which captures geometric information of the of the boundary including perimeter and the total horizontal mean curvature of the boundary of the domain. We use probabilistic method by studying the escaping probability of the horizon- tal Brownian motion process that is canonically associated to the sub-Riemannian structure of the Heisenberg group. This is a joint work with J. Tyson.