We have performed a study of thermally driven magnetic relaxation in building blocks of artificial kagome spin ice. For room-temperature measurements, we observe that low-energy states are accessed with high efficiency, particularly in structures with strong dipolar coupling and with low thicknesses. With carefully tuned heating experiments, we demonstrate how thermally active artificial spin ice systems relax magnetically from higher-energy states and eventually fall into low-energy states. The methods applied in our work offer the possibility to observe the thermodynamics of artificial spin ice systems in real space and time, and provide a way to directly investigate the nature of complex stochastic processes.