Quantum simulation is a highly ambitious program in cold atom research currently being pursued in laboratories worldwide. The goal is to use cold atoms in optical lattices to simulate models for unsolved strongly correlated systems, so as to deduce their properties directly from experimental data. An important step in this effort is to determine the temperature of the system, which is essential for deducing all thermodynamic functions. This step, however, remains difficult for lattice systems at the moment. Here, we propose a method based on a generalized fluctuation-dissipation theorem. It does not rely on numerical simulations and gives a universal thermometry scheme for quantum gas systems including mixtures and spinor gases, provided that the local density approximation is valid.