Climate science shows that the limitation of global warming requires a rapid transition towards net-zero emissions of green house gases (GHG) on a global scale. Expanding renewable power generation in a significant way is seen as an imperative measure within this transition. To compensate for the inherent volatility of wind- and solar-based power generation, flexible and dispatchable power generation technologies such as gas turbines are required. If operated with CO2-neutral fuels such as hydrogen or in combination with carbon capture plants, a GHG-neutral gas turbine operation could be achieved. An effective leverage to enhance carbon capture efficiency and a possible measure to safely burn hydrogen in gas turbines is the partial external recirculation of exhaust gas. By means of a model-based analysis of an industrial gas turbine, the present study initially assesses the thermodynamic impact caused by a fuel switch from natural gas to hydrogen. Although positive trends such as increasing net electrical power output and thermal efficiency can be observed, the overall effect on the gas turbine process is only minor. In a following step, the partial external recirculation of exhaust gas is evaluated and compared both for the combustion of natural gas and hydrogen, regardless of potential combustor design challenges. The influence of altering working fluid properties throughout the whole gas turbine process is thermodynamically evaluated for ambient temperature recirculation and recirculation at an elevated temperature. A reduction in thermal efficiency can be observed as well as non-negligible changes of relevant process variables. These changes are are more distinctive at a higher recirculation temperature.