  In this paper we present a comparison principle for higher order nonlinear
hypoelliptic heat operators on graded Lie groups. Moreover, using the
comparison principle we obtain blow-up type results and global in
$t$-boundedness of solutions of nonlinear equations for the heat
$p$-sub-Laplacian on stratified Lie groups. In particular, this paper
generalises and extends previous results obtained by the first author and
Suragan in [RS18].
