An approach for scaling end-pumped rod lasers to high output powers by employing a crystal with a continuously varying, nearly hyperbolic dopant concentration profile, resulting in a homogenization of the longitudinal temperature distribution, is presented. The crystal is characterized by determining its dopant concentration profile with an absorption measurement. The fluorescence upon spectrally narrow excitation is recorded, indicating the role of quenching of the upper laser level at high dopant concentration. The on-axis temperature distribution is calculated by employing a Fourier-Bessel approach for solving the stationary heat conduction equation, taking the temperature dependence of the heat conductivity and the dependence of the heat fraction on the dopant concentration into account. Experimentally, a maximum output power of 187W at an optical-to-optical efficiency of 53 \% has been demonstrated.