  In this paper, we investigate the long-time structure of the heat kernel on a
Riemannian manifold M which is asymptotically conic near infinity. Using
geometric microlocal analysis and building on results of Guillarmou and Hassell
on the low-energy resolvent, we give a complete description of the asymptotic
structure of the heat kernel in all spatial and temporal regimes. We apply this
structure to define and investigate a renormalized zeta function and
determinant of the Laplacian on M.
