In this paper we consider the semilinear parabolic equation ∑ i , j = 1 m a i j X i X j u − ∂ t u + V u p = 0 with a general class of potentials V = V ( ξ , t ) $V=V(\xi,t)$ , where A = { a i j } i , j is a positive definite symmetric matrix and the X i ’s denotes a system of left-invariant vector fields on a Carnot group G. Based on a fixed point argument and by establishing some new estimates involving the heat kernel, we study the existence and large-time behavior of global positive solutions to the preceding equation.