Superparamagnetic collections of thermally fluctuating nanomagnet moments undergo a dynamic freezing known as a blocking transition upon cooling. The collective behavior becomes more complex when neighboring nanomagnets interact, and is further complicated when the constituent material of the nanomagnets has a temperature-dependent magnetization. Such a system can exhibit loss of ergodicity or the development of long-range order, and is experimentally accessible in artificial spin ice arrays, which provide an excellent framework for investigating ergodicity loss and equilibration on laboratory timescales. Using a macrospin model and a non-standard Monte Carlo method, we describe the range of phase space that is thermally accessible, framing the problem within the context of the three relevant temperatures: the Curie temperature, the blocking temperature, and the collective ordering temperature of the nanomagnetic system. Our approach is generalizable and can be extended to a wide range of similar magnetic systems that are available for rigorous experimental tests.