The aim of this work is to clarify characteristics of time-dependent temperaltire behavior in a buoyant flow in stahly stratified air in an enclosure. For this aim, the two-dimensional, laminar, time-dependent continuity equation, Navier-Stokes equations with the buoyancy term, and energy equation are solved numerically by finite-difference methods. The computed results at unstratified condition agree well with the previous results, and validate the numerical accuracy. The present computational methods and procedures are therefore valid, and have sufficient grid resolution. As a result, at an odiahatic ceiling of the enclosure or in stably stratified air in the enclosure, a thermal cylinder with high temperature is discovered to occur intermittently near the plume front, and moves upward. However, a thermal cylinder never occurs at unstratified condition. Furthermore, a thermal cylinder exists in both the instantaneous cros.sover (COl) region at adiahatic condition and the timeaveraged crossover (COM) region at stratified condition. In other words, when a thermal cylinder exists, the region with a thermal cylinder is certainly either COM or COI.