We present numerical tests of the fluctuation-dissipation theorem (FDT) in the dumbbell model of spin ice with parameters suitable for dysprosium titanate. The tests are made for local spin variables, magnetic monopole density, and energy. We are able to achieve local equilibrium in which the FDT is satisfied down to $T=0.4\mathrm{K}$ below which the system completely freezes. Nonequilibrium dynamics, together with violation of the FDT, are nonetheless observed following a thermal quench into the noncontractable monopole pair regime. Despite FDT violation, an approximate linear response regime allows for the identification of effective nonequilibrium temperatures which are different for each variable. The spin variable appears hotter than the heat reservoir and the monopole concentration responds with a lower effective temperature, while the energy has a negative effective temperature. Results are discussed in the context of the monopole picture of spin ice and compared to the structure of FDT violations in other glassy materials. Prospectives for future experiments are reviewed.