The velocity field (i.e. the velocity distribution at all points in the space) and the temperature field in naturally ventilated spaces are of importance for several reasons. Both have an impact on thermal comfort. The velocity field has a direct bearing on the concentration field arising from sources of contaminants and on the age field. The temperature (density) field has an influence on envelope flows, by virtue of the resulting hydrostatic pressure distribution. However, one only has to look at the equations that govern the velocity and temperature at a point in a bounded three-dimensional space, and the complexity of the boundary conditions, to appreciate that there are no simple ways of determining the velocity and temperature fields in any detail. To obtain detail (in the sense of the values at all points in the space), it is necessary to make use of CFD or experimental measurement. The first of these approaches is the subject of Chapter 9 and experimental measurement is covered in Chapters 10 and 11.This raises the fundamental question of how important it is to know the full details of the velocity and temperature fields. This is particularly relevant to natural ventilation systems, because of the variations that arise naturally (from the variation of wind speed, direction and external temperature) and from occupant actions. An indication of the wide variation of the velocity field under wind-alone conditions can be obtained from dimensional analysis (Section 6.2.2). Such variations make it difficult to define representative design conditions, unlike mechanical ventilation, where the designer has closer control over the internal conditions.Bearing the above in mind, the aim of this chapter is to deal with theoretical methods for determining the velocity and temperature fields, but in less detail than what is possible with CFD and experimental measurement.The equations that govern the velocity and temperature at a point are described in Section 6.2, with a brief summary of the types of mathematical model that are available, namely zonal models, coarse-grid CFD and integrated zonal and envelope flow models.