Motivated by recent demands on regulatory reform, closed form solutions are developed for the filling times and upper layer temperatures for fires in large spaces including the volume expansion term that was neglected in previous similar efforts. The solutions evolve from (a) utilizing the air entrainment to a buoyant plume from a point source having the same convective heat release as the fire and (b) applying an energy balance for the hot layer. Heat losses to the Surfaces of the enclosure and provisions for smoke control by natural ventilation are also considered in an approximate way. Although analytic solutions for the filling times exist in the literature if the volume expansion term is neglected, this work is the first to (a) present analytic solutions for the upper layer temperature including the volume expansion term and (b) incorporate heat losses and smoke control by natural ventilation. The present, predictions agree with recent numerical results (Fire Sci. Technol. 19(1) (1999) 27), which agree with experimental data and consequently, the present results in turn agree well with experimental data (Fire Sci. Technol. 19(1) (1099) 27). They are also corroborated by asymptotic analysis worked out in Appendix A. For certain large spaces, the results show that critical times for evacuation or rescue operations from fire brigade depend on the upper layer temperature reaching high enough values to cause harm by radiation to occupants or fire fighting rescuers. Thus, critical times in large spaces do not result from the smoke layer descending below a critical height (e.g. 2.1 in from the floor), as they do for small spaces. The present results for large spaces having high ceiling clearance do not agree with CFAST calculations because the entrainment equation for the fire plume in CFAST is different from the one in this work. (C) 2004 Elsevier Ltd. All rights reserved.