Lattice Approximation of Quantum Statistical Traces at a Complex Temperature

We prove that the simple condition on the potential V, \int exp(-t V) < \infty for all t>0, is sufficient for the lattice approximation of the trace Tr[A exp(-b H)] with (Re b)>0 to work for all bounded functions A and a large class of potentials. As a by-product we obtain an explicit bound for the real-temperature lattice kernels.