  We study the quantization of the regularized hamiltonian, $H$, of the
compactified D=11 supermembrane with non-trivial winding. By showing that $H$
is a relatively small perturbation of the bosonic hamiltonian, we construct a
Dyson series for the heat kernel of $H$ and prove its convergence in the
topology of the von Neumann-Schatten classes so that $e^{-Ht}$ is ensured to be
of finite trace. The results provided have a natural interpretation in terms of
the quantum mechanical model associated to regularizations of compactified
supermembranes. In this direction, we discuss the validity of the Feynman path
integral description of the heat kernel for D=11 supermembranes and obtain a
matrix Feynman-Kac formula.
