The paper is concerned with the prediction of three-dimensional flow and heat transfer in enclosures of arbitrary complexity containing a fire source. The prediction method is based on a finite-difference solution of the three-dimensional fluid dynamic and heat/mass transfer field equations, with full effects of compressibility included and with modelling of the turbulent-buoyancy interactions. Results are presented for the temperature distributions and flow fields that develop during a fire in a typical shopping mall. These appear realistic. It is concluded that more work is required to validate the present model against experimental results; and that the successful application of a fully three-dimensional "field-model" to fire problems with multiple parameters does not any longer require prohibitively great computer power.