abstract: In this talk we will discuss the regularity of boundary points for the Dirichlet problem related to a class of linear degenerate-parabolic equations. We will show the validity of Wiener-type criteria for hypoelliptic operators with a fundamental solution satisfying suitable two-sided Gaussian bounds. The Wiener condition is expressed, in analogy with a result by Landis for the heat equation, in terms of a series of balayages. As an application, we will present a sharp sufficient condition of regularity for the case of the heat operators in Carnot groups. This is a joint work with F. Uguzzoni.