In lighting systems consisting light-emitting diodes (LEDs), excessive temperature is amain cause of degraded luminous efficacy, which leads to reduced average illuminance and distorted illumination rendering. Modeling the thermal dynamics of LEDs is hence essential in designing thermal dissipators and controllers for maintaining constant illuminance or chromaticity. In the existing literature, both physical modeling and system identification have been proposed, which all find the dependence of the temperature on the input power. When the power fluctuates, e.g., due to dimming control, the thermal dynamics becomes nonlinear. Moreover, when a photoelectrothermal model is used in the control synthesis, the nonlinearity due to the product of the temperature-dependent efficacy and the input power must be considered. These nonlinearities are either ignored or linearized in most existing methods. The main contribution of this work is treating the aforementioned nonlinearities in a linear parameter varying (LPV) framework. First, the nonlinear thermal dynamics is identified by LPV system identification techniques. Then, a controller to track reference illuminance is designed by H-infinity control techniques to be robust to both the temperature and the disturbance from ambient light. The identification data and the designed controller are collected from and verified on a real experimental setup.