This study examines the sustainability of roofs subjected to hot climate of Phoenix and cold climate of Montréal by using a validated numerical model that simultaneously solves the heat, air, and moisture equations. In many situations, the initial conditions needed to solve these equations are not available. This paper provides a procedure for conducting energy and moisture modelling so that using different initial conditions would result in no effect on the final results of roof performance. Additionally, the study focuses on: (a) assessing the moisture performance of black and cool roofs in case of using material layer with high initial construction moisture content (Fibreboard, FB), (b) identifying the time period needed so that the moisture content would reach acceptable limit by the building codes, and (c) determining the amount of energy savings as a result of using sustainable cool roofs instead of black roofs. The results show that the moisture content in the FB decreases to permissible levels after 92.6 days for black roof and 175.7 days for cool roof in Phoenix, while in Montréal, it takes 238.6 days and 1597 days, respectively. The effect of using different initial condition vanishes after 196 days for Phoenix’s black roof, 583 days for its cool roof, and 1247 days for Montréal’s black roof and 4590 days for its cool roof. Mold is detected in FB. In Phoenix, mold disappears after 379 days for black roof and 479 days for cool roof, whereas in Montréal, it takes 708 days and 3143 days, respectively.