The laser performance of resonantly pumped Er:YAG as the gain medium for an eye-safe high-power laser was investigated theoretically using a new thermo-optical model. The presented model takes into account the full spatially resolved temperature dependence of the most important parameters in the gain medium. Among those are the thermo-mechanical parameters (e.g. heat conduction), spectroscopic and multiphonon-relaxation lifetimes of the first four manifolds and the full spectral information of emission and absorption (4I15/2 ↔ 4I13/2) as well as excited-state absorption and re-emission (4I13/2 ↔ 4I9/2). All spectral lines are modeled as temperature dependent by calculating their line positions and line widths assuming two-phonon Raman interactions with the host. From these spectra the temperature dependent upconversion loss parameters can also be derived. The gain medium - cavity interaction is modeled by the rate equations for the first four manifolds and spectrally resolved radiation transport for pump and laser fields. Simultaneous solving this together with the heat generation and heat transport in the gain medium gives a realistic view into the Er:YAG laser performance. It predicts high optical-to-optical efficiences of > 60% at output powers of multiple kW from a single gain medium. The model is compared with experimental data of diode and fiber laser pumped Er:YAG lasers with good agreement.