We study formation and growth of human settlements as thermodynamic phenomena and focus on critical regimes associated with these processes. In doing so we develop a common thermodynamic perspective on modeling urban structures driven by "fast" and "slow" underlying dynamics of human resettlement and infrastructure development. The unifying perspective is illustrated by a comparative analysis of two qualitatively and quantitatively different models of dynamic resettlement. We demonstrate that the considered urban systems undergo phase transitions, irrespective of the particular details of the dynamic models. This suggests that the observed critical behavior is intrinsic to resettlement process.